A posteriori error estimation for arbitrary order FEM applied to singularly perturbed one-dimensional reaction-diffusion problems

Torsten Linß

Applications of Mathematics (2014)

  • Volume: 59, Issue: 3, page 241-256
  • ISSN: 0862-7940

Abstract

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FEM discretizations of arbitrary order r are considered for a singularly perturbed one-dimensional reaction-diffusion problem whose solution exhibits strong layers. A posteriori error bounds of interpolation type are derived in the maximum norm. An adaptive algorithm is devised to resolve the boundary layers. Numerical experiments complement our theoretical results.

How to cite

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Linß, Torsten. "A posteriori error estimation for arbitrary order FEM applied to singularly perturbed one-dimensional reaction-diffusion problems." Applications of Mathematics 59.3 (2014): 241-256. <http://eudml.org/doc/261112>.

@article{Linß2014,
abstract = {FEM discretizations of arbitrary order $r$ are considered for a singularly perturbed one-dimensional reaction-diffusion problem whose solution exhibits strong layers. A posteriori error bounds of interpolation type are derived in the maximum norm. An adaptive algorithm is devised to resolve the boundary layers. Numerical experiments complement our theoretical results.},
author = {Linß, Torsten},
journal = {Applications of Mathematics},
keywords = {reaction-diffusion problem; singular perturbation; mesh adaptation; reaction-diffusion problem; singular perturbation; mesh adaptation; finite element method},
language = {eng},
number = {3},
pages = {241-256},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A posteriori error estimation for arbitrary order FEM applied to singularly perturbed one-dimensional reaction-diffusion problems},
url = {http://eudml.org/doc/261112},
volume = {59},
year = {2014},
}

TY - JOUR
AU - Linß, Torsten
TI - A posteriori error estimation for arbitrary order FEM applied to singularly perturbed one-dimensional reaction-diffusion problems
JO - Applications of Mathematics
PY - 2014
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 59
IS - 3
SP - 241
EP - 256
AB - FEM discretizations of arbitrary order $r$ are considered for a singularly perturbed one-dimensional reaction-diffusion problem whose solution exhibits strong layers. A posteriori error bounds of interpolation type are derived in the maximum norm. An adaptive algorithm is devised to resolve the boundary layers. Numerical experiments complement our theoretical results.
LA - eng
KW - reaction-diffusion problem; singular perturbation; mesh adaptation; reaction-diffusion problem; singular perturbation; mesh adaptation; finite element method
UR - http://eudml.org/doc/261112
ER -

References

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  14. Roos, H.-G., Schopf, M., Convergence and stability in balanced norms of finite element methods on Shishkin meshes for reaction-diffusion problems, Z. Angew. Math. Mech., in press. 
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