A Robust Modified Weak Galerkin Finite Element Method for Reaction-Diffusion Equations

Abstract

In this paper, a robust modified weak Galerkin (MWG) finite element method for reaction-diffusion equations is proposed and investigated. An advantage of this method is that it can deal with the singularly perturbed reaction-diffusion equations. Another advantage of this method is that it produces fewer degrees of freedom than the traditional WG method by eliminating the element boundaries freedom. It is worth pointing out that, in our method, the test functions space is the same as the finite element space, which is helpful for the error analysis. Optimal-order error estimates are established for the corresponding numerical approximation in various norms. Some numerical results are reported to confirm the theory.