Remarks on balanced norm error estimates for systems of reaction-diffusion equations

Hans-Goerg Roos

Applications of Mathematics (2018)

  • Volume: 63, Issue: 3, page 273-279
  • ISSN: 0862-7940

Abstract

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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 H 1 seminorm leads to a balanced norm which reflects the layer behavior correctly. We discuss the difficulties which arise for systems of reaction-diffusion problems.

How to cite

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Roos, Hans-Goerg. "Remarks on balanced norm error estimates for systems of reaction-diffusion equations." Applications of Mathematics 63.3 (2018): 273-279. <http://eudml.org/doc/294436>.

@article{Roos2018,
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 $H^1$ seminorm leads to a balanced norm which reflects the layer behavior correctly. We discuss the difficulties which arise for systems of reaction-diffusion problems.},
author = {Roos, Hans-Goerg},
journal = {Applications of Mathematics},
keywords = {singular perturbation; finite element method; layer-adapted mesh; balanced norm},
language = {eng},
number = {3},
pages = {273-279},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Remarks on balanced norm error estimates for systems of reaction-diffusion equations},
url = {http://eudml.org/doc/294436},
volume = {63},
year = {2018},
}

TY - JOUR
AU - Roos, Hans-Goerg
TI - Remarks on balanced norm error estimates for systems of reaction-diffusion equations
JO - Applications of Mathematics
PY - 2018
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 63
IS - 3
SP - 273
EP - 279
AB - 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 $H^1$ seminorm leads to a balanced norm which reflects the layer behavior correctly. We discuss the difficulties which arise for systems of reaction-diffusion problems.
LA - eng
KW - singular perturbation; finite element method; layer-adapted mesh; balanced norm
UR - http://eudml.org/doc/294436
ER -

References

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