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

0086

Titel Englisch	Robust a posteriori error estimation for a singularly perturbed reaction-diffusion equation on anisotropic tetrahedral meshes
Autor	Gerd Kunert
Herausgeber	TU Chemnitz, SFB 393
Typ	Preprint
Sprache	Englisch
DDC-Sachgruppe(n)	510 004
Schlagwörter	· anisotropic solution · error estimator · reaction diffusion equation · singularly perturbed problem · stretched elements
Abstrakt Englisch	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.
Erstellungsdatum	2000-11-09
Speicherung seit	2000-11-09
Gültig bis	2020-11-09
Format	application/postscript
Grösse	360 KB
URL	http://archiv.tu-chemnitz.de/pub/2000/0086

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