The Dispersion in Finite Element Solutions to the One-Dimensional Heat Equation

Abstract

A method for evaluating the numerically introduced dispersion in finite element solutions to the one-dimensional heat equation is presented. The dispersion is quantified for linear and quadratic elements as a function of time step, mesh refinement and capacitance matrix formulation. It is demonstrated that an analysis of the dispersion is a useful tool in estimating the accuracy and in understanding the behavior of the numerical algorithm.