On the Discontinuous Galerkin Finite Element Method for Reaction-Diffusion Problems: Error Estimates in Energy and Balanced Norms
Provides theoretical error bounds for a numerical method solving singularly perturbed reaction-diffusion problems, which are important in fluid dynamics and chemical engineering.
The paper proves robust convergence of a nonsymmetric discontinuous Galerkin FEM for singularly perturbed reaction-diffusion problems using higher-order splines on layer-adapted meshes, with error estimates in energy and balanced norms.
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.