(Names of students are listed in bold.)
2023
Report 
Author(s)  Description  Link 
Date 
TRMATH 2302  G. Sosa Jones and C. Trenchea  Discrete energy balance equation via a symplectic secondorder method for twophase flow in porous media  October 2023  
TRMATH 2301  M. Edwards, M. Bukač, and C. Trenchea 
A secondorder partitioned method for bioconvective flows with concentration dependent viscosity 
June 2023 
2022
Report  Author(s)  Description  Link  Date 
TRMATH 2204  W. Layton, W. Pei and C. Trenchea  Time step adaptivity in the method of Dahlquist, Liniger and Nevanlinna  September 2022  
TRMATH 2203  F. Siddiqua and C. Trenchea 
A secondorder symplectic method for an advectiondiffusionreaction problem in bioseparation 
August 2022  
TRMATH 2202  M. Bukač, G. Fu, A. Seboldt and C. Trenchea 
Timeadaptive partitioned method for fluidstructure interaction problems with thick structures 
April 2022  
TRMATH 2201  A. Takhirov and C. Trenchea 
Efficient nonlinear filter stabilizationof the Lerayalpha model 
March 2022 
2021
Report  Author(s)  Description  Link  Date 
TRMATH 2101  M. Bukač and C. Trenchea  Adaptive, secondorder, unconditionally stable partitioned method for fluidstructure interaction  March 2021  
TRMATH 2102  J. Burkardt, W. Pei, and C. Trenchea  A stress test for the midpoint timestepping method  September 2021  
TRMATH 2103  W. Layton, W. Pei, and C. Trenchea  Refactorization of a variable step, unconditionally stable method of Dahlquist, Liniger and Nevanlinna  October 2021  
TRMATH 2104  A. Takhirov, C. Trenchea, and J. Waters 
Secondorder efficient nonlinear filter stabilization for high Reynolds number flows 
December 2021 
2020
Report  Author(s)  Description  Link  Date 
TRMATH 2003  M. Bukač, A. Seboldt and C. Trenchea  Refactorization of Cauchy’s method: a second– order partitioned method for fluid–thick structure interaction problems  August 2020  
TRMATH 2002  J. Burkardt and C. Trenchea  Refactorization of the midpoint rule  January 2020  
TRMATH 2001  W. Layton, W. Pei, Y. Qin and C. Trenchea  Analysis of the variable step method of Dahlquist, Liniger and Nevanlinna for fluid flow  January 2020 
2018
Report  Author(s)  Description  Link  Date 

TRMATH 1805

Y. Rong, W. Layton and H. Zhao  Extension of a simplified BaldwinLomax model of nonequilibrium turbulence: model, analysis and algorithms  December 2018  
TRMATH 1804  M.Bukač and C. Trenchea 
BOundary Update via Resolvent for fluidstructure interaction

October 2018  
TRMATH 1803  F. Diele, M. Garvie and C. Trenchea  Analysis of a secondorder in time implicitsymplectic scheme for predatorprey systems  August 2018  
TRMATH 1802

A. Guzel and W. Layton

Analysis of the time filters on the implicit method increased accuracy and improved stability  January 2018  
TRMATH 1801

O. Oyekole, M.Bukač and C. Trenchea

A secondorder in time approximation of fluid structure interaction problem  January 2018 
2017
Report  Author(s)  Description  Link  Date 

TRMATH 1702 
A. Guzel and C. Trenchea

The Williams step increases the stability and accuracy of the hoRA time filter  October 2017  
TRMATH 1701 
V. Ervin, M. Kubacki, W. Layton, M. Moraiti, Z. Si, C. Trenchea

Partitioned penalty methods for the evolutionary StokesDarcytransport problem  August 2017 
2016
Report  Author(s)  Description  Link  Date 

TRMATH 1603 
Yong Li, Catalin Trenchea

Existence and ergodicity for the twodimensional Boussinesq equation  December 2016  
TRMATH 1604  Roxana Tanase, Catalin Trenchea, and Ivan Yotov  Optimal Control of Systems Governed by PDEs with Random Parameter Fields  April 2016  
TRMATH 1601 
A. Vainchtein, Y. Starosvetsky, J. D. Wright, and R. Perline

Solitary waves in diatomic chains  March 2016  
TRMATH 1602 
L. Liu, G. James, P. Kevrekidis, and A. Vainchtein  Breathers in a locally resonant granular chain with precompression  March 2016 
2015
Report  Author(s)  Description  Link  Date 

TRMATH 1510 
V.J. Ervin, M. Kubacki, W. Layton, M. Moraiti, Z. Si, C. Trenchea 
On limiting behavior of contaminant transport models in coupled surface and groundwater flows  October 2015  
TRMATH 1505 
L. Liu, G. James, P. Kevrekidis and A. Vainchtein  Nonlinear waves in a strongly nonlinear resonant granular chain  June 2015  
TRMATH 1504 
A. Vainchtein, E. S. Van Vleck and A. Zhang  Propagation of periodic patterns in a discrete system with competing interactions  May 2015  
TRMATH 1503 
Y. Li and C. Trenchea  Partitioned second order method for magnetohydrodynamics in Elsasser fields  February 2015  
TRMATH 1502 
N. Jiang, M. Mohebujjaman, L.G.Rebholz, C.Trenchea  Analysis of a family of regularization methods for NavierStokes equations  January 2015  
TRMATH 1501 
Y. Li and C. Trenchea  Analysis of time filters used with the leapfrog scheme  January 2015 
2014
Report  Author(s)  Description  Link  Date 

TRMATH 1411 
H.A. Tran, C. Trenchea and C.G Webster  A convergence analysis of stochastic collocation method for NavierStokes equations with random input data  October 2014  
TRMATH 1410 
L. Truskinovsky and A. Vainchtein  Solitary waves in a nonintegrable FPU chain  September 2014  
TRMATH 1409 
N. Jiang, S. Kaya and W. Layton  Analysis of Model Variance for Ensemble Based Turbulence Modeling  May 2014  
TRMATH 1408 
N. Wilson, A. Labovsky, C. Trenchea  High accuracy method for magnetohydrodynamics system in Elsasser variables  May 2014  
TRMATH 1407 
W. Layton  The 1877 Boussinesq Conjecture: Turbulent Fluctuations are Dissipative on the Mean Flow  March 2014  
TRMATH 1406  W. Layton  2D Decaying Turbulence does not have Exponential Seperation of Trajectories  March 2014  
TRMATH 1405  C. Brucato  The Traveling Salesman Problem  January 2014  
TRMATH 1404  S. Jayasuriyay, S. Reichy and J. Wheeler  On the Iinverse ErdosHeilbronn Problem for Restricted Set Addition in Finite Groups  January 2014  
TRMATH 1403  N. Jiang  A Higher Order Ensemble Simulation Algorithm for Fluid Flows  January 2014  
TRMATH 1402  N. Jiang and H. Tran  Analysis of a stabilized CNLF method with fast slow wave splittings for flow problems  January 2014  
TRMATH 1401  Y. Li and P.D.Williams  Analysis of the RAW Filter in CompositeTendency Leapfrog Integrations  January 2014 
2013
Report  Author(s)  Description  Link  Date 

TRMATH 1301  N. Hurl, W. Layton, Y. Li and C. Trenchea  Stability Analysis of the CrankNicolsonLeapFrog Method with the RobertAsselinWilliams Time Filter  January 2013  
TRMATH 1302  W. Layton, H. Tran and C. Trenchea  Numerical Analysis of two Partitioned Methods for Uncoupling Evolutionary MHD Flows  January 2013  
TRMATH 1303  M. Kubacki and M. Moraiti  Analysis of a Second Order, Unconditionally Stable, Partitioned Method for the Evolutionary StokesDarcy Problem  January 2013  
TRMATH 1304  C. Lupu  Mean value theorems of Flett type for a Volterra operator  February 2013  
TRMATH 1305  L. Liu, A. Vainchtein, Y. Wang  Kinetics of a Twinning Step  March 2013  
TRMATH 1306  N. Jiang and W. Layton  An Algorithm for Fast Calculation of Flow Ensembles  April 2013  
TRMATH 1315  W. Layton and L.G. Rebholz 
On Relaxation Times in the NavierStokesVoigt Model 
April 2013  
TRMATH 1307 
B. Espinoza, P. Gartside and A. Mametelashvili 
nArc Connected Spaces  May 2013  
TRMATH 1308 
S. P. Hastings and J. B McLeod 
Uniqueness of Relaxation Oscillations: A Classical Approach  June 2013  
TRMATH 1309 
N. Jiang and W. Layton 
Numerical Analysis of two Ensemble Eddy Viscosity Models of Fluid Motion  July 2013  
TRMATH 1310 
N. Hurl, W. Layton, Y. Li and M. Moraiti 
The Unstable Mode in the CrankNicolson LeapFrog Method is Stable 
August 2013  
TRMATH 1311 
W. Layton and A. Takhirov 
Energy Stability Of A First Order Partitioned Method For Systems With General Coupling

August 2013  
TRMATH 1312 
N. Jiang and W. Layton 
Further Numerical Tests of Ensemble Eddy Viscosity Methods

August 2013  
TRMATH 1313 
W. Layton, A. Takhirov and M. Sussman 
Instability of CrankNicolson LeapFrog for Nonautonomous Systems 
August 2013  
TRMATH 1314 
A. Takhirov 
Exact Solution of the Stochastic NavierStokes Equations 
August 2013  
TRMATH 1315 
N. Jiang, M. Kubacki, W. Layton, M. Moraiti and H. Tran 
A CrankNicolson LeapFrog stabilization: 
September 2013  
TRMATH 1316 
Y. Li and C. Trenchea 
A higherorder RobertAsselin type time filter 
September 2013  
TRMATH 1317 
M. Bukač, W. Layton, M. Moraiti, H. Tran and C. Trenchea 
Analysis of partitioned methods for Biot system 
October 2013 
2012
Report  Author(s)  Description  Link  Date 

TRMATH 1201  W. Layton  The Interior Error of Van Cittert Deconcolution of Differential Filters is Optimal  January 2012  
TRMATH 1202 
W. Layton 
Introduction to the Transfer theory of Turbulence  Januray 2012  
TRMATH 1203  M. Moraiti  On the Quasistatic Approximation in the StokesDarcy Model of GroundwaterSurface Water Flows 
March 2012  
TRMATH 1204  C. Trenchea  Stability of Partitioned Imex Methods for Systems of Evolution Equations with SkewSymmetric Coupling  April 2012  
TRMATH 1205

C. Trenchea  Unconditional Stability of a Partitioned Imex Method for Magnetohydrodynamic Flows  April 2012  
TRMATH 1206 
V. Girault, D. Vassilev and I. Yotov 
Mortar Multiscale Finite Element Methods for StokesDarcy Flows 
April 2012  
TRMATH 1207  M. Kubacki  Uncoupling Evolutionary GroundwaterSurface Water Flows Using the CrankNicolson Leapfrog Method  April 2012  
TRMATH 1208  P. Rosakis and A. Vainchtein  New Solutions for Slow Moving Kinks in a Forced FrenkelKontorova Chain  May 2012  
TRMATH 1209  A. Jorgenson  Unconditional Stability of a CrankNicolson AdamsBashforth 2 ImplicitExplicit Numerical Method  May 2012  
TRMATH 1210  C. Trenchea  Second Order Implicit for Local Effects and Explicit for Nonlocal Effects is Unconditionally Stable  May 2012  
TRMATH 1211  W. Layton and A. Takhirov  A Test of a Modular, Wall Adapted Nonlinear Filter Model for Underresolved Flows  June 2012  
TRMATH 128  C. Lupu and V. Matei  Arithmetic Functions, Prime Counting Function and Polynomials  July 2012  
TRMATH 1214  N. Hurl  Energy Stability of the CrankNicolson Leap Frog Method with Time Filters 
October 2012  
TRMATH 1215  X. Xiong  Analysis of a MultiRate Splitting Method for Uncoupling Evolutionary GroundwaterSurfacewater Flows  October 2012  
TRMATH 1216  A. Takhirov  StokesBrinkman Lagrange Multiplier/Fictitious Domain Method for Flows in Pebble Bed Geometries  October 2012  
TRMATH 1219  N. Costea, D. A. Ion and C. Lupu  Variationallike Inequality Problems Involving SetValued Maps and Generalized Monotonicity  October 2012  
TRMATH 1217  P.G. Kevrekidis, A. Vainchtein, M. Serra Garcia, and C. Daraio  Interaction of Traveling Waves with MassWithMass Defects within a Hertzian Chain  December 2012 
2011
Report  Author(s)  Description  Link  Date 

TRMATH 1101  L. Shan, H. Zheng and W. Layton  Decoupled scheme with different time step sizes for the evolutionary StokesDarcy model  January 2011  
TRMATH 1102 
W. Layton, C. Trenchea 
Stability of two IMEX methods, CNLF and BDF2AB2, for uncoupling systems of evolution equations  February 2011  
TRMATH 1103  L. Shan, H. Zheng and W. Layton  A NonIterative, Domain Decomposition Method with Different Time Step Sizes for the Evolutionary StokesDarcy Model  May 2011  
TRMATH 1104  L. Shan and H. Zheng  Partitioned Time Stepping Method for Fully Evolutionary StokesDarcy Flow with BeaversJoseph Interface 
May 2011  
TRMATH 1105  W. Layton, H. Tran and C. Trenchea  Analysis of Long Time Stability and Errors of Two Partitioned Methods for Uncoupling Evolutionary Groundwater  Surface Water Flows 
May 2011  
TRMATH 1106  G. Yuksel and R. Ingram  Numerical Analysis of a Finite Element, CrankNicolson Discretization for MHD Flows at Small Magnetic Reynolds Numbers 
May 2011  
TRMATH 1107  R. Ingram  A New Linearly Extrapolated CrankNicolson TimeStepping Scheme for the NSE  July 2011  
TRMATH 1108  A. Vainchtein and P. G. Kevrekidis  Dynamics of phase transitions in a piecewise linear diatomic chain  September 2011  
TRMATH 1109  A. Bowers, L. Rebholz, A. Takhirov, and C. Trenchea  Improved Accuracy in Regularization Models of Iincompressible Flow Via Adaptive Nonlinear Filtering 
October 2011  
TRMATH 1110  W. Layton, N. Mays, M. Neda and C. Trenchea  Numerical Analysis of Modular Regularization Methods for the BDF2 Time Discretization of the NavierStokes Equations 
November 2011  
TRMATH 1111  W. Layton, H. Tran and X. Xiong  Long Time Stability of Four Methods for Splitting the Evolutionary StokesDarcy Problem into Stokes and Darcy Subproblems  November 2011 
2010
Report  Author(s)  Description  Link  Date 

TRMATH 1001  V. Ervin, W. Layton and M. Neda  Numerical Analysis of Filter Based Stabilization for Evolution Equations  January 2010  
TRMATH 1002  J. Arciero, G. Ermentrout, J. Upperman, Y. Vodovotz, J. Rubin  Using a Mathematical Model to Analyze the Role of Probiotics and Inflammation in Necrotizing Enterocolitis  January 2010  
TRMATH 1003 
E. Manica, G. Medvedev and J. Rubin  First Return Maps for the Dynamics of Synaptically Coupled Conditional Bursters 
January 2010  
TRMATH 1004  H. Tran  On the Estimates of Determining Modes for NSalpha and NSomega Models 
January 2010  
TRMATH 1005  E. Trofimov and A. Vainchtein  Shocks versus kinks in a discrete model of displacive phase transitions  February 2010  
TRMATH 1006  B. Ganis, I. Yotov and M. Zhong  A Stochastic Mortar Mixed Finite Element Method for Flow in Porous Media with Multiple Rock Types 
April 2010  
TRMATH 1007  A. Labovschii and C. Trenchea  Approximate Deconvolution Models for Magnetohydrodynamics  April 2010  
TRMATH 1008  S. Hritz  Phenomenology and Computations of a Regularization of the NavierStokes Equations Related to a NonNewtonian Fluid Flow Model  May 2010  
TRMATH 1009 
R. Ingram  Unconditional convergence of highorder extrapolations of the CrankNicolson, nite element method for the NavierStokes equations 
July 2010  
TRMATH 1010  W. Layton, L. Rebholz and C. Trenchea  Modular Nonlinear Filter Stabilization of Methods for Higher Reynolds Numbers Flow  September 2010  
TRMATH 1011 
W. Layton, M. Neda and K. Wyss 
A Transfer Theory Analysis of Approximate Deconvolution Models of Turbulence 
October 2010  
TRMATH 1012  W. Layton, L. Roehe and H. Tran  Explicitly Uncoupled VMS Stabilization of Fluid Flow  November 2010  
TRMATH 1013  M. Sussman  A Stability Examble  November 2010  
TRMATH 1014  K. Lipnikov, D. Vassilev and I. Yotov  Discontinuous Galerkin and Mimetic Finite Difference Methods for Coupled StokesDarcy Flows on Polygonal and Polyhedral Grids  November 2010  
TRMATH 1015  M. Wheeler, G. Xue and I. Yotov  A Multiscale Mortar Multipoint Flux Mixed Finite Element Method  December 2010  
TRMATH 1016  M. Wheeler, G. Xue and I. Yotov  A multipoint flux mixed finite element method on distorted quadrilaterals and hexahedra  December 2010  
TRMATH 1017  W. Layton, L. Shan and H. Zheng 
Numerical Analysis of Modular VMS Methods with Nonlinear Eddy Viscosity for the NaiverStokes Equations 
December 2010 
2009
Report  Author(s)  Description  Link  Date 

TRMATH 0901  J. Connors  Convergence analysis and computational testing of the finite element discretization of the NavierStokesalpha model  January 2009  
TRMATH 0902  X. Hu AND D. Wang  Low Mach Number Limit of Viscous Compressible Magnetohydrodynamic Flows 
February 2009  
TRMATH 0903  C. Manica and I. Stanculescu  Numerical Analysis of LerayTikhonov Deconvolution Models of Fluid Motion 
Feburary 2009  
TRMATH 0904  J. Connors and A. Labovsky  High Accuracy Semiimplicit Spectral Deffered Correction Decoupling Methods for a Parabolic Two Domain Problem  February 2009  
TRMATH 0905  B. Doubrov, J. Holland and G. Sparling 
Spacetime and G2  February 2009  
TRMATH 0906  A. Lozovskiy  Numerical Analysis of the Semidiscrete Finite Element Method for Computing the Noise Generated by Turbulent Flows 
February 2009  
TRMATH 0907  S. VerduzcoFlores, M. Bodner, G.B. Ermentrout, J. M. Fuster, YD. Zhou 
Working memory cells’ behavior may be explained by crossregional networks with synaptic facilitation 
February 2009  
TRMATH 0908  S. VerduzcoFlores, B. Ermentrout and M. Bodner  From working memory to epilepsy: Dynamics of facilitation and inhibition in a cortical network 
February 2009  
TRMATH 0910  P. Hajlasz and Z. Liu  A Compact Embedding of a Sobolev Space is Equivalent to an Embedding into a Better Space 
March 2009  
TRMATH 0911  A. Vainchtein and E. Van Vleck  Nucleation and propagation of phase mixtures in a bistable chain  March 2009  
TRMATH 0912  B. Ganis and I. Yotov  Implementation of a Mortar Mixed Finite Element Method using a Multiscale Flux Basis  March 2009  
TRMATH 0913  B Layton and A Novoyny  On Lighthill's acoustic analogy for low Mach number flows  April 2009  
TRMATH 0914  J. Day, J. Rubin and C. Chow  Competition Between Transients in the Rate of Approach to a Fixed Point 
April 2009  
TRMATH 0915  G. Chen, M. Slemrod and D. Wang  Weak Continuity of the GaussCodazziRicci System for Isometric Embedding  May 2009  
TRMATH 0916  X. Hu and D. Wang  Global Strong Solution to the DensityDependent Incompressible Viscoelastic Fluids 
May 2009  
TRMATH 0917  L. Truskinovsky and A. Vaninchtein  Beyond Kinetic Relations  May 2009  
TRMATH 0918  S. Kubota, J. Rubin and T. Kitajima  Modulation of LTP/LTD balance in STDP by activitydependent feedback mechanism 
May 2009  
TRMATH 0919  A. Vainchtein  The Role of Spinodal Region in the Kinetics of Lattice Phase Transitions  May 2009  
TRMATH 0920  T. Stepien  Tubuloglomerular FeedbackMediated Dynamics in Three Coupled Nephrons 
May 2009  
TRMATH 0921  S. Bayrama, T. Stepien, and E. Pitman  TGFMediated Dynamics in a System of Many Coupled Nephrons 
May 2009  
TRMATH 0922  R. Ingram  A Mixed Finite Element Approximation of StokesBrinkman and NSBrinkman Equation for NonDarcian Flows  July 2009  
TRMATH 0923  W. Layton and C. Trenchea  The DasMoser Commutator Closure for Filtering Through a Boundary is Well Posed  July 2009  
TRMATH 0924  R. Ingram, M. Wheeler and I. Yotov  A multipoint flux mixed finite element method on hexahedra'' by Ross Ingram, Mary F. Wheeler  July 2009  
TRMATH 0925  M. Garvie, P. Maini and C Trenchea  A Methodology for Parameter Identification in Turing Systems 
August 2009  
TRMATH 0926  M. F. Wheeler, T. Wildey, and I. Yotov  A multiscale preconditioner for stochastic mortar mixed finite elements  August 2009  
TRMATH 0927  W. Layton  On Taylor/Eddy Solutions of Approximate Deconvolution Models of Turbulence  August 2009  
TRMATH 0928  A. Vainchtein  Effect of nonlinearity on the steady motion of a twinning dislocation  September 2009  
TRMATH 0929  W. Layton, C. Pruett and L. Rebholz  Temporally Regularized Direct Numerical Simulation 
October 2009  
TRMATH 0930  W. Layton  FluidPorous Interface Conditions with the "Inertia Term" 1/2 UFLUID2 are not Galilean Invariant  October 2009  
TRMATH 0931  A. Lozovskiy  Numerical Analysis of the Fully Discrete Finite Element Scheme for the Lighthill Acoustic Analogy and Estimating the Errorin the Sound Power 
October 2009  
TRMATH 0932  G. Ermentrout, J. Jalics and J. Rubin  Stimulusdriven traveling solutions in continuum neuronal models with a general smooth firing rate function 
December 2009  
TRMATH 0933  J. Dunmyre and J. Rubin  Optimal Intrinsic Dynamics for Bursting in a ThreeCell Network  December 2009  
TRMATH 0934  C. Frias  Comparison of turbulence models using OPENFOAM

December 2009 
2008
Report  Author(s)  Description  Link  Date 

TRMATH 0801  W. Layton, C. Manica, M. Neda and L. Rebholz  Numerical Analysis and Computational comparisons of the NSalpha and NSomegaregularizations  January 2008  
TRMATH 0802  W. Layton and I. Stanculescu  Chebychev optimized approximate deconvolution models of turbulence  January 2008  
TRMATH 0803  X. Hu and D. Wang  Global existence and largetime behavior of solutions to the threedimensional equations of compressible magnetohydrodynamics flows  January 2008  
TRMATH 0804  X. Hu and D. Wang  Global solutions to the threedimensional full compressible magnetohydrodynamics flows  January 2008  
TRMATH 0805  X. Hu and D. Wang  Compactness of weak solutions to the threedimensional compressible magnetohydrodynamics flows  January 2008  
TRMATH 0806  A. Reynolds, J. Rubin, G. Clermont, J. Day, Y. Vodovotz, G. B. Ermentrout 
A reduced mathematical model of the acute inflammatory response: 
February 2008  
TRMATH 0807  J. Day, J. Rubin, Y. Vodovotz, C. Chow, A. Reynolds, G. Clermont 
A reduced mathematical model of the acute inflammatory response II. Capturing scenarios of repeated endotoxin administration 
February 2008  
TRMATH 0808  K. Lipnikov, M. Shashkov, and I. Yotov  Local flux mimetic finite difference methods  February 2008  
TRMATH 0809 
B. Ganis, H. Klie, M. F. Wheeler, T. Wildey, I. Yotov, and D. Zhang  Stochastic collocation and mixed finite elements for flow in porous media  February 2008  
TRMATH 0810  V. Girault, S. Sun, M. Wheeler, And I. Yotov  Coupling discontinuous Galerkin and mixed finite element discretizations using mortar finite elements  February 2008  
TRMATH 0811  G. Pencheva and I. Yotov  Interior superconvergence in mortar and nonmortar mixed finite element methods on nonmatching grids  March 2008  
TRMATH 0812  J. Day, J. Rubin and C. Chow  Competition Between Transients in the Rate of Approach to a Fixed Point  March 2008  
TRMATH 0813  W. Layton, L. Rebholz and M. Sussman  Energy and Helicity Dissipation Rates of the NSAlpha and NSAlphaDeconvolution Models  March 2008  
TRMATH 0814  S. P. Hastings and J. B. McLeod  An Elementary Approach to a Model Problem of Lagerstrom 
April 2008  
TRMATH 0815  B. Ermentrout and S.P. Hastings  Steady state analysis of a continuum model for superinfection.  April 2008  
TRMATH 0816  S. Dauna, J. Rubin, Y. Vodovotz, A. Roye, R. Parkere and G. Clermont  An Ensemble of Models of the Acute Inflammatory Response to Bacterial Lipopolysaccharide in Rats: Results from Parameter Space Reduction  April 2008  
TRMATH 0817  A. Cesmelioglu and B. Riviere  Analysis of TimeDependent NavierStokes Flow Coupled with Darcy Flow  May 2008  
TRMATH 0818  W. Layton, I. Stanculescu and C. Trenchea  Theory of the NSomega model: A Compliment to the NSalpha Model  June 2008  
TRMATH 0819  J. Connors and W. Layton  On the Accuracy of the Finite Element Method Plus Time Relaxation  June 2008  
TRMATH 0820  W. Layton, C. Manica, M. Neda, M. Olshanskii and L. Rebholz  On the Accurate of the Rotation form in Simulations of the Navier Stokes Equations  June 2008  
TRMATH 0821  S. Daun, J. Rubin and I. Rybak  Control of Oscillation Periods and Phase Durations in HalfCentral Pattern Generators: a Comparative Mechanistic Analysis  July 2008  
TRMATH 0827  P. Gartside and Z. Feng  Spaces with a Finite Family of Basic Functions  July 2008  
TRMATH 0822  D. Vassilev and I. Yotov  Coupling StokesDarcy Flow with Transport  August 2008  
TRMATH 0823  R. Ingram, W. Layton and N. Mays  Analysis of Iterated Tikhonov: Defect Correction for IllPosed Problems  August 2008  
TRMATH 0828  L. Chism, X. He, L. Huang, A. Ibrahim, C. Jones, Y. Shu, C. Wah Wu, Z. Fu 
Performance study of peertopeer video streaming on complex networks 
August 2008  
TRMATH 0824  M. Garvie and C. Trenchea  The Identification of Space Time Distributed Parameters in ReactionDiffusion Systems  September 2008  
TRMATH 0825  W. Layton  Existence of Smooth Attractors for the NavierStokesOmega Model of Turbulence: Expanded Version 
December 2008  
TRMATH 0826  J. Conners, J. Howell and W. Layton  Partitioned Timestepping For a Parabolic Two Domain Problem  December 2008 
2007
Report  Author(s)  Description  Link  Date 

TRMATH 0701  W. Layton and R. Lewandowski  A high accuracy Leraydeconvolution model of turbulence and its limiting behavior  January 2007  
TRMATH 0702  W. Layton and I. Stanculescu  K41 optimized approximate deconvolution models  January 2007  
TRMATH 0703  P. Lindqvist and J.J. Manfredi  Viscosity supersolutions of the evolutionary pLaplace equation  February 2007  
TRMATH 0704  S. Zenker, J. Rubin, and G. Clermont  Towards a model based medicine: a clinically meaningful approach to illposed inverse problems in quantitative physiology  February 2007  
TRMATH 0705  W. Layton  A remark on regularity of an ellipticelliptic singular perturbation problem  February 2007  
TRMATH 0706  B. Lal Sharma and A. Vainchtein  Quasistatic propagation of steps along a phase boundary  March 2007  
TRMATH 0707  Y. Zhen and A. Vainchtein  Dynamics of steps along a martensitic phase boundary I: semianalytical solution  March 2007  
TRMATH 0708  Y. Zhen and A. Vainchtein  Dynamics of steps along a martensitic phase boundary II: numerical simulations  March 2007  
TRMATH 0709  V. Girault and B. Riviere  DG approximation of coupled NavierStokes and Darcy equations by BeaverJosephSaffman interface condition  March 2007  
TRMATH 0710  S. Chanillo and J. J. Manfredi  Sharp global bounds for the Hessian on pseudohermitian manifolds  April 2007 

TRMATH 0711  A. Borisov, M. Dickinson and S. Hastings  A congruence problem for polyhedra  April 2007 

TRMATH 0712  S. Hastings, D. Kinderlehrer, J.B. McLeod  Diffusion mediated transport in multiple state systems  April 2007 

TRMATH 0721  P. Gartside and Z. Feng  More stratifiable function spaces  April 2007  
TRMATH 0722  Z. Feng and R. Heath  Metrizability of Topological Semigroups on Linearly Ordered Topological Spaces  April 2007  
TRMATH 0713  P.Chidyagwai and B. Riviere  A weak solution and a multinumerics solution of the coupled NavierStokes and Darcy equations  August 2007  
TRMATH 0714  A. Labovschii  A Defect Correction Method for the TimeDependent NavierStokes Equations  August 2007  
TRMATH 0715 
A. Labovschii, W. Layton, C. Manica, M. Neda, L. Rebholz  The Stabilized, Extrapolated Trapezoidal Finite Element Method for the NavierStokes Equations  August 2007  
TRMATH 0716  A. Labovschii, C. Trenchea  Large Eddy Simulation for MHD Flows  August 2007  
TRMATH 0717 
I. Stanculescu

Existence Theory of Abstract Approximate Deconvolution Models of Turbulence  August 2007  
TRMATH 0718 
A. Labovschii, 
Mathematical Architecture of Approximate Deconvolution Models of Turbulence  September 2007  
TRMATH 0719  L. Truskinovsky, A. Vainchtein  Dynamics of martensitic phase boundaries: discreteness, dissipation and inertia 
October 2007  
TRMATH 0720  A. Labovschii  A Defect Correction Method for the Evolutionary Convection Diffusion Problem with Increased Time Accuracy 
October 2007 
2006
Report  Author(s)  Description  Link  Date 

TRMATH 0601  Y. Epshteyn, T. Khan, and B. Riviere  Inverse problem in optical tomography using discontinuous Galerkin method  January 2006  
TRMATH 0602  L. Rebholz  An energy and helicity conserving finite element scheme for the NavierStokes equations  January 2006  
TRMATH 0603  J. Rubin and A. Bose  The geometry of neuronal recruitment  February 2006  
TRMATH 0604  V. John, W. Layton, and C. Manica  Convergence of time averaged statistics of finite element approximations of the NavierStokes equations  February 2006  
TRMATH 0605  Y. Epshteyn and B. Riviere  Symmetric interior penalty Galerkin methods for elliptic problems  February 2006  
TRMATH 0606  V. Ervin, W. Layton, and M. Neda  Numerical analysis of a higher order time relaxation model of fluids  February 2006  
TRMATH 0607  J. Proft and B. Riviere  Analytical and numerical study of diffusive fluxes for transport equations with neardegenerate coefficients  April 2006  
TRMATH 0608  J. Rubin  Bursting induced by excitatory synaptic coupling in nonidentical conditional relaxation oscillators or squarewave bursters  April 2006  
TRMATH 0609  W. Layton and M. Neda  A similarity theory of approximate deconvolution models of turbulence  May 2006  
TRMATH 0610  W. Layton, C. Manica, M. Neda, and L. Rebholz  The joint helicityenergy cascade for homogeneous, isotropic turbulence generated by approximate deconvolution models  May 2006  
TRMATH 0611  C. Manica and S. Kaya Merdan  New discretizations of turbulent flow problems  May 2006  
TRMATH 0612  C. Manica and S. Kaya Merdan  Convergence analysis of the finite element method for a fundamental model in turbulence  May 2006  
TRMATH 0613  W. Layton  Bounds on energy and helicity dissipation rates of approximate deconvolution models of turbulence  June 2006  
TRMATH 0614  P. Lindqvist and J. Manfredi  Note on a remarkable superposition for a nonlinear equation  July 2006  
TRMATH 0615  T. Arbogast, G. Pencheva, M.F. Wheeler, and I. Yotov  A multiscale mortar mixed finite element method  July 2006  
TRMATH 0616  W. Layton  Superconvergence of finite element discretization of time relaxation models of advection  August 2006  
TRMATH 0617  Y. Epshteyn and B. Riviere  Analysis of hp discontinuous Galerkin methods for incompressible twophase flow  September 2006  
TRMATH 0618  M. Neda and B. Riviere  Discontinuous finite elements for solving the StolzAdams approximate deconvolution model for turbulent flows  October 2006  
TRMATH 0619  L. Rebholz  A family of new high order NSalpha models arising from helicity correction in Leray turbulence models  November 2006  
TRMATH 0620  J. Rubin and M. Wechselberger  Giant squidhidden canard: the 3D geometry of the HodkinHuxley model  November 2006  
TRMATH 0621  W. Layton, C. Manica, M. Neda, and L. Rebholz  Numerical analysis and computational testing of a high accuracy Leraydeconvolution model of turbulence  November 2006 
2005
Report  Author(s)  Description  Link  Date 

TRMATH 0501  S. Kaya, W. Layton, and B. Riviere  Subgrid stabilized defect correction methods for the NavierStokes equations  February 2005  
TRMATH 0502  V. John, S. Kaya, and W. Layton  A twolevel variational multiscale method for convectiondiffusion equations  February 2005  
TRMATH 0503  W. Layton and R. Lewandowski  An exposition on the timeaveraged accuracy of approximate deconvolution, large eddy simulation models of turbulence  February 2005  
TRMATH 0504  J. Best, A. Borisyuk, J. Rubin, D. Terman, and M. Wechselberger  The dynamic range of bursting in a network of synaptically coupled squarewave bursting respiratory pacemaker cells  February 2005  
TRMATH 0505  W. Layton and R. Lewandowski  Residual stress of approximate deconvolution models of turbulence  April 2005  
TRMATH 0506  M.F. Wheeler and I. Yotov  A multipoint flux mixed finite element method  July 2005  
TRMATH 0507  Y. Epshteyn and B. Riviere  Fully implicit discontinuous Galerkin schemes for multiphase flow  June 2005  
TRMATH 0508  L. Truskinovsky and A. Vainchtein  Quasicontinuum models of dynamic phase transitions  July 2005  
TRMATH 0509  L. Rebholz  A multiscale VP discretization for flow problems  September 2005  
TRMATH 0510  W. Klieber and B. Riviere  Adaptive simulations of twophase flow by discontinuous Galerkin methods  October 2005  
TRMATH 0511  L. Rebholz  Conservation laws of turbulence models  October 2005  
TRMATH 0512  G. Pencheva  On some numerical convergence studies of mixed finite element methods for flow in porous media  November 2005  
TRMATH 0513  K. Lipnikov, M. Shashkov, and I. Yotov  Local flux mimetic finite difference methods  November 2005  
TRMATH 0514  I. Aavatsmark, G.T. Eigestad, R.A. Klausen, M.F. Wheeler, and I. Yotov  Convergence of a symmetric MPFA method on quadrilateral grids  November 2005  
TRMATH 0515  W. Layton and M. Neda  Truncation of scales by time relaxation  November 2005  
TRMATH 0516  J. Rubin and K. Josic  The firing of an excitable neuron in the presence of stochastic trains of strong synaptic inputs  November 2005  
TRMATH 0517  G. Pencheva and I. Yotov  Changes in UTPRODJ3D: a threedimension multiblock mixedhybrid finite element code  November 2005  
TRMATH 0518  T. Russel, M.F. Wheeler, and I. Yotov  Superconvergence for controlvolume mixed finite element methods on rectangular grids  Nov. 2005  
TRMATH 0519  M.F. Wheeler and I. Yotov  A cellcentered finite difference method on quadrilaterals  November 2005 
2004
Report  Author(s)  Description  Link  Date 

TRMATH 0401  J. Rubin and A. Bose  Localized activity pattern in excitatory neuronal networks  February 2004  
TRMATH 0402  B. Riviere  Numerical study of a discontinuous Galerkin method for incompressible twophase flow  March 2004  
TRMATH 0403  L. Truskinovsky and A. Vainchtein  Quasicontinuum modeling of shortwave instabilities in crystal lattices  April 2004  
TRMATH 0404  K. Josic and J. Rubin  Deriving information about architecture from activity patterns in coupled cell systems  April 2004  
TRMATH 0405  W. Layton and R. Lewandowski  On a wellposed turbulence model  August 2004  
TRMATH 0406  S. Kaya and B. Riviere  A twogrid stabilization method for solving the steadystate NavierStokes equations  August 2004  
TRMATH 0407  W. Layton and R. Lewandowski  Consistency and feasibility of approximate deconvolution models of turbulence  August 2004  
TRMATH 0408  V. Girault, B. Riviere, and M. Wheeler  A splitting method using discontinuous Galerkin for the transient incompressible NavierStokes equations  September 2004  
TRMATH 0409  L. Truskinovsky and A. Vainchtein  Kinetics of martensitic phase transitions: lattice model  October 2004 
2003
Report  Author(s)  Description  Link  Date 

TRMATH 0301  J. Su, J. Rubin, and D. Terman  Effects of noise on elliptic bursters  January 2003  
TRMATH 0302  W. Layton  Model reduction by constraints, discretization of flow problems and an induced pressure stabilization  January 2003  
TRMATH 0303  W. Layton  A mathematical introduction to large Eddy simulation  January 2003  
TRMATH 0304  S. Kaya  Numerical analysis of a subgrid scale Eddy viscosity method for higher Reynolds number flow problems  January 2003  
TRMATH 0305  S. Kaya and W. Layton  Subgridscale eddy viscosity methods are variational multiscale methods  January 2003  
TRMATH 0306  V. John, W. Layton, and N. Sahin  Derivation and analysis of near wall models for channel and recirculating flows  February 2003  
TRMATH 0307  L. Truskinovsky and A. Vainchtein  About the origin of the nucleation peak in transformational plasticity  April 2003  
TRMATH 0308  B. Riviere and I. Yotov  Locally conservative coupling of Stokes and Darcy flows  May 2003  
TRMATH 0309  M. Kaya  Existence of weak solutions for a scalesimilarity model of the motion of large eddies in turbulent flow  July 2003  
TRMATH 0310  J. Drover, J. Rubin, J. Su, and B. Ermentrout  Analysis of a canard mechanism by which excitatory synaptic coupling can synchronize neurons at low firing frequencies  July 2003  
TRMATH 0311  B. Riviere  Analysis of a discontinuous finite element method for the coupled Stokes and Darcy problems  July 2003  
TRMATH 0312  L. Truskinovsky and A. Vainchtein  Explicit kinetic relation from "first principles"  August 2003  
TRMATH 0313  G.M. Constantine  On the partial orthogonality of faithful characters  August 2003  
TRMATH 0314  S. Kaya and B. Riviere  Analysis of a discontinuous Galerkin and eddy viscosity method for NavierStokes  September 2003  
TRMATH 0315  Y.B. Altundas and G. Caginalp  Computations of dendrites in 3D and comparison with microgravity experiments  September 2003  
TRMATH 0316  R.C. Read and E.G. Whitehead Jr.  A note on chain lengths and the Tutte polynomial  October 2003  
TRMATH 0317  M. Anitescu, W.J. Layton, and F. Pahlevani  Implicit for local effects and explicit for nonlocal effects is unconditionally stable  October 2003  
TRMATH 0318  A. Dunca and Y. Epshteyn  On the AdamsStolz deconvolution LES models  October 2003 
2002
Report  Author(s)  Description  Link  Date 

TRMATH 0201  P. Bastian and B. Riviere  Superconvergence and H(div) projection for discontinuous Galerkin methods  September 2002  
TRMATH 0202  G. Pencheva and I. Yotov  Balancing domain decomposition for mortar mixed finite element methods  October 2002  
TRMATH 0203  T.C. Hales  The honeycomb problem on the sphere  November 2002  
TRMATH 0204  J. Gordon and T.C. Hales  Virtual transfer factors  November 2002  
TRMATH 0205  A. Caglar  Weak imposition of boundary conditions for the NavierStokes equations  November 2002  
TRMATH 0206  L. Truskinovsky and A. Vainchtein  PeierlsNabarro landscape for martensitic phase transitions  December 2002  
TRMATH 0207  T.C. Hales  Orbital integrals are motivic  December 2002 
Report  Author(s)  Description  Link  Date 
TRMATH 2101  M. Bukač and C. Trenchea  Adaptive, secondorder, unconditionally stable partitioned method for fluidstructure interaction  March 2021  
TRMATH 2102  J. Burkardt, W. Pei, and C. Trenchea  A stress test for the midpoint timestepping method  September 2021  
TRMATH 2103  W. Layton, W. Pei, and C. Trenchea  Refactorization of a variable step, unconditionally stable method of Dahlquist, Liniger and Nevanlinna  October 2021  
TRMATH 2104  A. Takhirov, C. Trenchea, and J. Waters 
Secondorder efficient nonlinear filter stabilization for high Reynolds number flows 
December 2021 