Error Estimates in Balanced Norms of Finite Element Methods for Higher Order Reaction-Diffusion Problems

Abstract

Error estimates of finite element methods for reaction-diffusion problems are often realised in the related energy norm. In the singularly perturbed case, however, this norm is not adequate. A different scaling of the $H$^$m$ seminorm for 2$m$-th order problems leads to a balanced norm which reflects the layer behaviour correctly. We prove error estimates in such balanced norms and improve thereby existing estimates known in literature.