ON TAYLOR WEAK STATEMENT FINITE-ELEMENT METHODS FOR COMPUTATIONAL FLUID-DYNAMICS

A Taylor series augmentation of a weak statement (a 'Taylor weak state ment' or 'Taylor-Galerkin' method) is used to systematically reduce th e dispersion error in a finite element approximation of the one-dimens ional transient advection equation. A frequency analysis is applied to determine the phase velocity of semi-implicit linear, quadratic and c ubic basis one-dimensional finite element methods and of several compa rative finite difference/finite volume algorithms. The finite element methods analysed include both Galerkin and Taylor weak statements. The frequency analysis is used to obtain an improved linear basis Taylor weak statement finite element algorithm. Solutions are reported for ve rification problems in one and two dimensions and are compared with fi nite volume solutions. The improved finite element algorithms have suf ficient phase accuracy to achieve highly accurate linear transient sol utions with little or no artificial diffusion.