Stability and Phase Speed for Various Finite Element Formulations of the Advection Equation

Abstract

This paper analyzes the stability and accuracy of various finite element approximations to the linearized two-dimensional advection equation. Four triangular elements with linear basis functions are included along with a rectangular element with bilinear basis functions. In addition, second-and fourth-order finite difference schemes are examined for comparison. Time is discretized with the leapfrog method. The criss-cross triangle formulation is found to be unstable. The best schemes are the isosceles triangles with linear basis functions and the rectangles with bilinear basis functions.