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Error Estimates in Balanced Norms of Finite Element Methods on Shishkin Meshes for Reaction-Diffusion Problems

https://doi.org/10.18255/1818-1015-2016-3-357-363

Abstract

Error estimates of finite element methods for reaction-diffusion problems are often realized in the related energy norm. In the singularly perturbed case, however, this norm is not adequate. A different scaling of the H1 seminorm leads to a balanced norm which reflects the layer behavior correctly.

About the Author

R. Hans-G.
Institut fuЁr Numerische Mathematik, Technische UniversitaЁt Dresden, 01062 Dresden, Deutschland
Russian Federation


References

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5. Roos H.-G., Schopf M., “Convergence and stability in balanced norms of finite element methods on Shishkin meshes for reaction-diffusion problems”, ZAMM, 95(6) (2015), 551– 565.


Review

For citations:


Hans-G. R. Error Estimates in Balanced Norms of Finite Element Methods on Shishkin Meshes for Reaction-Diffusion Problems. Modeling and Analysis of Information Systems. 2016;23(3):357-363. (In Russ.) https://doi.org/10.18255/1818-1015-2016-3-357-363

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ISSN 1818-1015 (Print)
ISSN 2313-5417 (Online)