A Weak Galerkin Finite Element Method for Singularly Perturbed Convection-Diffusion--Reaction Problems

Abstract

In this article, a new weak Galerkin finite element method is introduced to solve convection-diffusion--reaction equations in the convection dominated regime. Our method is highly flexible by allowing the use of discontinuous approximating functions on polytopal mesh without imposing extra conditions on the convection coefficient. An error estimate is devised in a suitable norm. Numerical examples are provided to confirm theoretical findings and efficiency of the method.