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

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.

Author Details

Sebastian Franz

Hans-G. Roos