On the Solution of the Time-Dependent Convection-Diffusion Equation by the Finite Element Method

Abstract

A Petrov-Galerkin finite element method is presented for the time-dependent convection-diffusion equation. The scheme is based on bilinear time-space trial and quadratic in time-linear in space test functions, the latter being non-conforming.
Secondorder in time and third order in space accuracy is obtained, and the schemesare free of numerical diffusion and dispersion effects. Numerical results are presented
which show excellent approximation properties.