Finite Difference and Discontinuous Galerkin Methods for Fully Nonlinear Second Order PDEs

Tuesday, February 18, 2014 - 10:00 to 11:00
427 Thackeray Hall
Speaker Information
Thomas Lewis
The University of North Carolina at Greensboro

Abstract or Additional Information

A convergence framework for directly approximating the viscosity solutions of fully nonlinear second order PDE problems will be discussed.  The main focus will be the introduction of a set of sufficient conditions for constructing convergent finite difference (FD) methods.  The conditions given are meant to be easier to realize and implement than those found in the current literature.  The given FD methodology will then be shown to generalize to a class of discontinuous Galerkin (DG) methods.  The proposed DG methods allow for high order and increased flexibility when choosing a computational mesh.  Numerical experiments will be presented to gauge the performance of the proposed DG methods.  An overview of the PDE theory of viscosity solutions will also be given. 

Research Area