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Robust a posteriori error estimation for a singularly perturbed reaction-diffusion equation on anisotropic tetrahedral meshes

We consider a singularly perturbed reaction-diffusion problem and
derive and rigorously analyse an a posteriori residual error
estimator that can be applied to anisotropic finite element meshes.

The quotient of the upper and lower error bounds is the so-called
matching function which depends on the anisotropy (of the
mesh and the solution) but not on the small perturbation parameter.
This matching function measures how well the anisotropic finite
element mesh corresponds to the anisotropic problem.
Provided this correspondence is sufficiently good, the matching
function is O(1).
Hence one obtains tight error bounds, i.e. the error estimator
is reliable and efficient as well as robust with respect to the
small perturbation parameter.

A numerical example supports the anisotropic error analysis.

Identiferoai:union.ndltd.org:DRESDEN/oai:qucosa.de:bsz:ch1-200000867
Date09 November 2000
CreatorsKunert, Gerd
ContributorsTU Chemnitz, SFB 393
PublisherUniversitätsbibliothek Chemnitz
Source SetsHochschulschriftenserver (HSSS) der SLUB Dresden
LanguageEnglish
Detected LanguageEnglish
Typedoc-type:preprint
Formatapplication/pdf, application/postscript, text/plain, application/zip

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