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

Error estimates in balanced norms of finite element methods for higher order reaction-diffusion problems