Error Estimates in Balanced Norms of Finite Element Methods for Higher Order Reaction-Diffusion Problems
Year: 2020
Author: Sebastian Franz, Hans-G. Roos
International Journal of Numerical Analysis and Modeling, Vol. 17 (2020), Iss. 4 : pp. 532–542
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2020-IJNAM-17868
International Journal of Numerical Analysis and Modeling, Vol. 17 (2020), Iss. 4 : pp. 532–542
Published online: 2020-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 11
Keywords: Balanced norms reaction-diffusion problems finite element methods.