Stability analysis of the forward Euler scheme for the convection‐diffusion equation using the SUPG formulation in space

Abstract

The stability and accuracy of the forward Euler scheme for the semidiscrete problem arising from the space discretization of the convection‐diffusion equation using the SUPG formulation are analysed. Both linear and quadratic finite elements are considered. The stability limits are derived for the one‐dimensional problem and a heuristic criterion is proposed for the multidimensional equation. Some numerical experiments are conducted in order to assess the performance of different finite elements.