University of Pittsburgh

Technical Reports

(Names of students listed in bold.)

2008

Report Author(s) Description Link Date
TR-MATH 08-01 W. Layton, C. Manica, M. Neda and L. Rebholz Numerical Analysis and Computational comparisons of the NS-alpha and NS-omegaregularizations PDF January 2008
TR-MATH 08-02 W. Layton and I. Stanculescu Chebychev optimized approximate deconvolution models of turbulence PDF January 2008
TR-MATH 08-03 X. Hu and D. Wang Global existence and large-time behavior of solutions to the three-dimensional equations of compressible magnetohydrodynamics flows PDF January 2008
TR-MATH 08-04 X. Hu and D. Wang Global solutions to the three-dimensional full compressible magnetohydrodynamics flows PDF January 2008
TR-MATH 08-05 X. Hu and D. Wang Compactness of weak solutions to the three-dimensional compressible magnetohydrodynamics flows PDF January 2008
TR-MATH 08-06 A. Reynolds, J. Rubin, G. Clermont, J. Day, Y. Vodovotz, G. B. Ermentrout

A reduced mathematical model of the acute inflammatory response:
I. Derivation of model and analysis of anti-inflammation

PDF February 2008
TR-MATH 08-07 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
PDF February 2008
TR-MATH 08-08 K. Lipnikov, M. Shashkov, and I. Yotov Local flux mimetic finite difference methods PDF February 2008

TR-MATH 08-09

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 PDF February 2008
TR-MATH 08-10 V. Girault, S. Sun, M. Wheeler, And I. Yotov Coupling discontinuous Galerkin and mixed finite element discretizations using mortar finite elements PDF February 2008
TR-MATH 08-11 G. Pencheva and I. Yotov Interior superconvergence in mortar and non-mortar mixed finite element methods on non-matching grids PDF March 2008
TR-MATH 08-12 J. Day, J. Rubin and C. Chow Competition Between Transients in the Rate of Approach to a Fixed Point PDF March 2008
TR-MATH 08-13 W. Layton, L. Rebholz and M. Sussman Energy and Helicity Dissipation Rates of the NS-Alpha and NS-Alpha-Deconvolution Models PDF March 2008
TR-MATH 08-14 S. P. Hastings and J. B. McLeod An Elementary Approach to a Model Problem of
Lagerstrom
PDF April 2008
TR-MATH 08-15 B. Ermentrout and S.P. Hastings Steady state analysis of a continuum model for super-infection. PDF April 2008
TR-MATH 08-16 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 PDF April 2008

2007

Report Author(s) Description Link Date
TR-MATH 07-01 W. Layton and R. Lewandowski A high accuracy Leray-deconvolution model of turbulence and its limiting behavior PDF January 2007
TR-MATH 07-02 W. Layton and I. Stanculescu K-41 optimized approximate deconvolution models PDF January 2007
TR-MATH 07-03 P. Lindqvist and J.J. Manfredi Viscosity supersolutions of the evolutionary p-Laplace equation PDF February 2007
TR-MATH 07-04 S. Zenker, J. Rubin, and G. Clermont Towards a model based medicine: a clinically meaningful approach to ill-posed inverse problems in quantitative physiology PDF February 2007
TR-MATH 07-05 W. Layton A remark on regularity of an elliptic-elliptic singular perturbation problem PDF February 2007
TR-MATH 07-06 B. Lal Sharma and A. Vainchtein Quasistatic propagation of steps along a phase boundary PDF March 2007
TR-MATH 07-07 Y. Zhen and A. Vainchtein Dynamics of steps along a martensitic phase boundary I: semi-analytical solution PDF March 2007
TR-MATH 07-08 Y. Zhen and A. Vainchtein Dynamics of steps along a martensitic phase boundary II: numerical simulations PDF March 2007
TR-MATH 07-09 V. Girault and B. Riviere DG approximation of coupled Navier-Stokes and Darcy equations by Beaver-Joseph-Saffman interface condition PDF March 2007
TR-MATH 07-10 S. Chanillo and J. J. Manfredi Sharp global bounds for the Hessian on pseudo-hermitian manifolds PDF April
2007
TR-MATH 07-11 A. Borisov, M. Dickinson and S. Hastings A congruence problem for polyhedra PDF
Code
April
2007
TR-MATH 07-12 S. Hastings, D. Kinderlehrer, J.B. McLeod Diffusion mediated transport in multiple state systems PDF April
2007
TR-MATH 07-13 P.Chidyagwai and B. Riviere
A weak solution and a multinumerics solution of the coupled Navier-Stokes and Darcy equations PDF August 2007
TR-MATH 07-14 A. Labovschii A Defect Correction Method for the Time-Dependent Navier-Stokes Equations PDF August 2007

TR-MATH 07-15

A. Labovschii, W. Layton, C. Manica, M. Neda, L. Rebholz The Stabilized, Extrapolated Trapezoidal Finite Element Method for the Navier-Stokes Equations PDF August 2007
TR-MATH 07-16 A. Labovschii, C. Trenchea Large Eddy Simulation for MHD Flows PDF August 2007
TR-MATH 07-17

I. Stanculescu

Existence Theory of Abstract Approximate Deconvolution Models of Turbulence PDF August 2007
TR-MATH 07-18

A. Labovschii,
W. Layton, C. Manica, M. Neda, L. Rebholz,
I. Stanculescu, C. Trenchea

Mathematical Architecture of Approximate Deconvolution Models of Turbulence PDF September 2007
TR-MATH 07-19 L. Truskinovsky, A. Vainchtein Dynamics of martensitic phase boundaries: discreteness,
dissipation and inertia
PDF October 2007
TR-MATH 07-20 A. Labovschii A Defect Correction Method for the Evolutionary
Convection Diffusion Problem with Increased Time Accuracy
PDF October 2007

2006

Report Author(s) Description Link Date
TR-MATH 06-01 Y. Epshteyn, T. Khan, and B. Riviere Inverse problem in optical tomography using discontinuous Galerkin method PDF January 2006
TR-MATH 06-02 L. Rebholz An energy and helicity conserving finite element scheme for the Navier-Stokes equations PDF January 2006
TR-MATH 06-03 J. Rubin and A. Bose The geometry of neuronal recruitment PDF February 2006
TR-MATH 06-04 V. John, W. Layton, and C. Manica Convergence of time averaged statistics of finite element approximations of the Navier-Stokes equations PDF February 2006
TR-MATH 06-05 Y. Epshteyn and B. Riviere Symmetric interior penalty Galerkin methods for elliptic problems PDF February 2006
TR-MATH 06-06 V. Ervin, W. Layton, and M. Neda Numerical analysis of a higher order time relaxation model of fluids PDF February 2006
TR-MATH 06-07 J. Proft and B. Riviere Analytical and numerical study of diffusive fluxes for transport equations with near-degenerate coefficients PDF April 2006
TR-MATH 06-08 J. Rubin Bursting induced by excitatory synaptic coupling in non-identical conditional relaxation oscillators or square-wave bursters PDF April 2006
TR-MATH 06-09 W. Layton and M. Neda A similarity theory of approximate deconvolution models of turbulence PDF May 2006
TR-MATH 06-10 W. Layton, C. Manica, M. Neda, and L. Rebholz The joint helicity-energy cascade for homogeneous, isotropic turbulence generated by approximate deconvolution models PDF May 2006
TR-MATH 06-11 C. Manica and S. Kaya Merdan New discretizations of turbulent flow problems PDF May 2006
TR-MATH 06-12 C. Manica and S. Kaya Merdan Convergence analysis of the finite element method for a fundamental model in turbulence PDF May 2006
TR-MATH 06-13 W. Layton Bounds on energy and helicity dissipation rates of approximate deconvolution models of turbulence PDF June 2006
TR-MATH 06-14 P. Lindqvist and J. Manfredi Note on a remarkable superposition for a nonlinear equation PDF July 2006
TR-MATH 06-15 T. Arbogast, G. Pencheva, M.F. Wheeler, and I. Yotov A multiscale mortar mixed finite element method PDF July 2006
TR-MATH 06-16 W. Layton Superconvergence of finite element discretization of time relaxation models of advection PDF August 2006
TR-MATH 06-17 Y. Epshteyn and B. Riviere Analysis of hp discontinuous Galerkin methods for incompressible two-phase flow PDF September 2006
TR-MATH 06-18 M. Neda and B. Riviere Discontinuous finite elements for solving the Stolz-Adams approximate deconvolution model for turbulent flows PDF October 2006
TR-MATH 06-19 L. Rebholz A family of new high order NS-alpha models arising from helicity correction in Leray turbulence models PDF November 2006
TR-MATH 06-20 J. Rubin and M. Wechselberger Giant squid-hidden canard: the 3D geometry of the Hodkin-Huxley model PDF November 2006
TR-MATH 06-21 W. Layton, C. Manica, M. Neda, and L. Rebholz Numerical analysis and computational testing of a high accuracy Leray-deconvolution model of turbulence PDF November 2006

2005

Report Author(s) Description Link Date
TR-MATH 05-01 S. Kaya, W. Layton, and B. Riviere Subgrid stabilized defect correction methods for the Navier-Stokes equations PDF February 2005
TR-MATH 05-02 V. John, S. Kaya, and W. Layton A two-level variational multiscale method for convection-diffusion equations PDF February 2005
TR-MATH 05-03 W. Layton and R. Lewandowski An exposition on the time-averaged accuracy of approximate de-convolution, large eddy simulation models of turbulence PDF February 2005
TR-MATH 05-04 J. Best, A. Borisyuk, J. Rubin, D. Terman, and M. Wechselberger The dynamic range of bursting in a network of synaptically coupled square-wave bursting respiratory pacemaker cells PDF February 2005
TR-MATH 05-05 W. Layton and R. Lewandowski Residual stress of approximate deconvolution models of turbulence PDF April 2005
TR-MATH 05-06 M.F. Wheeler and I. Yotov A multipoint flux mixed finite element method PDF July 2005
TR-MATH 05-07 Y. Epshteyn and B. Riviere Fully implicit discontinuous Galerkin schemes for multiphase flow PDF June 2005
TR-MATH 05-08 L. Truskinovsky and A. Vainchtein Quasicontinuum models of dynamic phase transitions PDF July 2005
TR-MATH 05-09 L. Rebholz A multiscale V-P discretization for flow problems PDF September 2005
TR-MATH 05-10 W. Klieber and B. Riviere Adaptive simulations of two-phase flow by discontinuous Galerkin methods PDF October 2005
TR-MATH 05-11 L. Rebholz Conservation laws of turbulence models PDF October 2005
TR-MATH 05-12 G. Pencheva On some numerical convergence studies of mixed finite element methods for flow in porous media PDF November 2005
TR-MATH 05-13 K. Lipnikov, M. Shashkov, and I. Yotov Local flux mimetic finite difference methods PDF November 2005
TR-MATH 05-14 I. Aavatsmark, G.T. Eigestad, R.A. Klausen, M.F. Wheeler, and I. Yotov Convergence of a symmetric MPFA method on quadrilateral grids PDF November 2005
TR-MATH 05-15 W. Layton and M. Neda Truncation of scales by time relaxation PDF November 2005
TR-MATH 05-16 J. Rubin and K. Josic The firing of an excitable neuron in the presence of stochastic trains of strong synaptic inputs PDF November 2005
TR-MATH 05-17 G. Pencheva and I. Yotov Changes in UTPRODJ3D: a three-dimension multiblock mixed-hybrid finite element code PDF November 2005
TR-MATH 05-18 T. Russel, M.F. Wheeler, and I. Yotov Superconvergence for control-volume mixed finite element methods on rectangular grids PDF Nov. 2005
TR-MATH 05-19 M.F. Wheeler and I. Yotov A cell-centered finite difference method on quadrilaterals PDF November 2005

2004

Report Author(s) Description Link Date
TR-MATH 04-01 J. Rubin and A. Bose Localized activity pattern in excitatory neuronal networks PDF February 2004
TR-MATH 04-02 B. Riviere Numerical study of a discontinuous Galerkin method for incompressible two-phase flow PDF March 2004
TR-MATH 04-03 L. Truskinovsky and A. Vainchtein Quasicontinuum modeling of short-wave instabilities in crystal lattices PDF April 2004
TR-MATH 04-04 K. Josic and J. Rubin Deriving information about architecture from activity patterns in coupled cell systems PDF April 2004
TR-MATH 04-05 W. Layton and R. Lewandowski On a well-posed turbulence model PDF August 2004
TR-MATH 04-06 S. Kaya and B. Riviere A two-grid stabilization method for solving the steady-state Navier-Stokes equations PDF August 2004
TR-MATH 04-07 W. Layton and R. Lewandowski Consistency and feasibility of approximate deconvolution models of turbulence PDF August 2004
TR-MATH 04-08 V. Girault, B. Riviere, and M. Wheeler A splitting method using discontinuous Galerkin for the transient incompressible Navier-Stokes equations PDF September 2004
TR-MATH 04-09 L. Truskinovsky and A. Vainchtein Kinetics of martensitic phase transitions: lattice model PDF October 2004

2003

Report Author(s) Description Link Date
TR-MATH 03-01 J. Su, J. Rubin, and D. Terman Effects of noise on elliptic bursters PDF January 2003
TR-MATH 03-02 W. Layton Model reduction by constraints, discretization of flow problems and an induced pressure stabilization PDF January 2003
TR-MATH 03-03 W. Layton A mathematical introduction to large Eddy simulation PDF January 2003
TR-MATH 03-04 S. Kaya Numerical analysis of a subgrid scale Eddy viscosity method for higher Reynolds number flow problems PDF January 2003
TR-MATH 03-05 S. Kaya and W. Layton Subgrid-scale eddy viscosity methods are variational multiscale methods PDF January 2003
TR-MATH 03-06 V. John, W. Layton, and N. Sahin Derivation and analysis of near wall models for channel and recirculating flows PDF February 2003
TR-MATH 03-07 L. Truskinovsky and A. Vainchtein About the origin of the nucleation peak in transformational plasticity PDF April 2003
TR-MATH 03-08 B. Riviere and I. Yotov Locally conservative coupling of Stokes and Darcy flows PDF May 2003
TR-MATH 03-09 M. Kaya Existence of weak solutions for a scale-similarity model of the motion of large eddies in turbulent flow PDF July 2003
TR-MATH 03-10 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 PDF July 2003
TR-MATH 03-11 B. Riviere Analysis of a discontinuous finite element method for the coupled Stokes and Darcy problems PDF July 2003
TR-MATH 03-12 L. Truskinovsky and A. Vainchtein Explicit kinetic relation from "first principles" PDF August 2003
TR-MATH 03-13 G.M. Constantine On the partial orthogonality of faithful characters PDF August 2003
TR-MATH 03-14 S. Kaya and B. Riviere Analysis of a discontinuous Galerkin and eddy viscosity method for Navier-Stokes PDF September 2003
TR-MATH 03-15 Y.B. Altundas and G. Caginalp Computations of dendrites in 3-D and comparison with microgravity experiments PDF September 2003
TR-MATH 03-16 R.C. Read and E.G. Whitehead Jr. A note on chain lengths and the Tutte polynomial PDF October 2003
TR-MATH 03-17 M. Anitescu, W.J. Layton, and F. Pahlevani Implicit for local effects and explicit for nonlocal effects is unconditionally stable PDF October 2003
TR-MATH 03-18 A. Dunca and Y. Epshteyn On the Adams-Stolz deconvolution LES models PDF October 2003

2002

Report Author(s) Description Link Date
TR-MATH 02-01 P. Bastian and B. Riviere Superconvergence and H(div) projection for discontinuous Galerkin methods PDF September 2002
TR-MATH 02-02 G. Pencheva and I. Yotov Balancing domain decomposition for mortar mixed finite element methods PDF October 2002
TR-MATH 02-03 T.C. Hales The honeycomb problem on the sphere PDF November 2002
TR-MATH 02-04 J. Gordon and T.C. Hales Virtual transfer factors PDF November 2002
TR-MATH 02-05 A. Caglar Weak imposition of boundary conditions for the Navier-Stokes equations PDF November 2002
TR-MATH 02-06 L. Truskinovsky and A. Vainchtein Peierls-Nabarro landscape for martensitic phase transitions PDF December 2002
TR-MATH 02-07 T.C. Hales Orbital integrals are motivic PDF December 2002