A note on the energy norm for a singularly perturbed model problem

Description

A singularly perturbed reaction-diffusion model problem is considered, and the choice of an appropriate norm is discussed. Particular emphasis is given to the energy norm. Certain prejudices against this norm are investigated and disproved. Moreover, an adaptive finite element algorithm is presented which exhibits an optimal error decrease in the energy norm in some simple numerical experiments. This underlines the suitability of the energy norm.

Links & Downloads

1. urn:nbn:de:bsz:ch1-200100062
2. https://monarch.qucosa.de/id/qucosa%3A17672
3. https://monarch.qucosa.de/api/qucosa%3A17672/attachment/ATT-0/
4. https://monarch.qucosa.de/api/qucosa%3A17672/attachment/ATT-1/
5. https://monarch.qucosa.de/api/qucosa%3A17672/attachment/ATT-2/
6. https://monarch.qucosa.de/api/qucosa%3A17672/attachment/ATT-3/

Tags

info:eu-repo/classification/ddc/510

ddc:510

singularly perturbed problem

reaction diffusion equation

adaptive algorithm

error estimator

Additional Fields

Identifer	oai:union.ndltd.org:DRESDEN/oai:qucosa:de:qucosa:17672
Date	16 January 2001
Creators	Kunert, Gerd
Publisher	Technische Universität Chemnitz
Source Sets	Hochschulschriftenserver (HSSS) der SLUB Dresden
Language	English
Detected Language	English
Type	doc-type:preprint, info:eu-repo/semantics/preprint, doc-type:Text
Rights	info:eu-repo/semantics/openAccess