Volume 17, Issue 4
Error Estimates in Balanced Norms of Finite Element Methods for Higher Order Reaction-Diffusion problems

Sebastian FranzHans-G. Roos

Int. J. Numer. Anal. Mod., 17 (2020), pp. 532-542.

Published online: 2020-08

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  • 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.

  • Keywords

Balanced norms, reaction-diffusion problems, finite element methods.

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COPYRIGHT: © Global Science Press

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@Article{IJNAM-17-532, author = {Franz , Sebastian and Roos , Hans-G.}, title = {Error Estimates in Balanced Norms of Finite Element Methods for Higher Order Reaction-Diffusion problems}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2020}, volume = {17}, number = {4}, pages = {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.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/17868.html} }
TY - JOUR T1 - Error Estimates in Balanced Norms of Finite Element Methods for Higher Order Reaction-Diffusion problems AU - Franz , Sebastian AU - Roos , Hans-G. JO - International Journal of Numerical Analysis and Modeling VL - 4 SP - 532 EP - 542 PY - 2020 DA - 2020/08 SN - 17 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/17868.html KW - Balanced norms, reaction-diffusion problems, finite element methods. AB -

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.

Sebastian Franz & Hans-G. Roos. (2020). Error Estimates in Balanced Norms of Finite Element Methods for Higher Order Reaction-Diffusion problems. International Journal of Numerical Analysis and Modeling. 17 (4). 532-542. doi:
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