Convergence and stability in balanced norms of finite element methods on Shishkin meshes for reaction-diffusion problems

Error estimates of finite element methods for reaction-diffusion problems are often realized in the related energy norm. In the singularly perturbed case, however, this norm is not adequate. A different scaling of the H-1 seminorm leads to a balanced norm which reflects the layer behavior correctly. We prove error estimates in balanced norms and investigate also stability questions. Especially, we propose a new C-0 interior penalty method with improved stability properties in comparison with the Galerkin FEM. (C) 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim