A Piecewise Linear Finite Element Discretization of the Diffusion Equation

Teresa Bailey, Texas A&M University

A piecewise linear (PWL) finite element spatial discretization has been developed for the multi-dimensional diffusion equation. It uses piecewise linear weight and basis functions in the finite element approximation. This method can solve the diffusion equation on arbitrary polygonal (2D) or polyhedral (3D) grids, which allows for the solution of problems with complex shapes. My presentation will describe the implementation of the PWL method into an existing diffusion code that is part of the KULL project at Lawrence Livermore National Laboratory. The new method, which generates a symmetric positive definite coefficient matrix, will be compared against the existing method, which is a vertex-centered discretization with an asymmetric coefficient matrix.

Abstract Author(s): Teresa S. Bailey and Marvin L. Adams