Enriched finite element methods for unsteady reaction-diffusion problems

摘要

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.