Enriched finite element methods for unsteady reaction–diffusion problems

Abstract

Abstract We develop enriched finite element methods for parabolic singularly perturbed problems. A Petrov–Galerkin strategy is employed, where the test and the trial spaces are enriched with ‘bubble’ and multiscale functions, respectively. We examine two semi‐discrete formulations for the unsteady reaction–diffusion equation, namely the method of lines and a variation of it inspired by the Rothe method. Numerical tests validate the approaches. Copyright © 2005 John Wiley & Sons, Ltd.