On the Discontinuous Galerkin Finite Element Method for Reaction-Diffusion Problems: Error Estimates in Energy and Balanced Norms

Abstract

A nonsymmetric discontinuous Galerkin FEM with interior penalties has been applied to one-dimensional singularly perturbed reaction-diffusion problems. Using higher order splines on Shishkin-type layer-adapted meshes and certain graded meshes, robust convergence has been proved in the corresponding energy norm and in a balanced norm. Numerical experiments support theoretical findings.