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 solves the radiation diffusion equation on arbitrary polyhedral 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 finite volume discretization with an asymmetric coefficient matrix. We will show that the new method retains many of the same convergence properties of the old method, and that both methods are able to handle difficult problems.

Abstract Author(s): Teresa Bailey, Texas A&M University <br />Marvin Adams, Texas A&M University<br />Brian Yang, Lawrence Livermore National Laboratory