Error estimates in balanced norms of finite element methods for higher order reaction-diffusion problems
For researchers working on numerical methods for singularly perturbed reaction-diffusion problems, this provides improved error estimates that correctly reflect layer behavior.
The paper proves error estimates in balanced norms for finite element methods applied to higher-order reaction-diffusion problems, improving upon existing estimates in the literature.
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 $2m$-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.