STABILITY AND PHASE SPEED FOR VARIOUS FINITE ELEMENT FORMULATIONS OF THE ADVECTION EQUATION

This pa.per analyzes the stability and accuracy of various finite element approxima-tion;,: Lo the linearized two-dimensional ad vection equation. Four tria.ngula.r clements>vith linear basis functions are included along with a rectangular element with bilin-p;u basis functions. In addition, second-and fourth-order finitP ditferencP schPmes;up Pxarnined for comparison. Time is discrPtized ·with thP IPapfrog met.hod. 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.