A Review of Unified A Posteriori Finite Element Error Control
- This paper aims at a general guideline to obtain a posteriori error estimates for the finite element error control in computational partial differential equations. In the abstract setting of mixed formulations, a generalised formulation of the corresponding residuals is proposed which then allows for the unified estimation of the respective dual norms. Notably, this can be done with an approach which is applicable in the same way to conforming, nonconforming and mixed discretisations. Subsequently, the unified approach is applied to various model problems. In particular, we consider the Laplace, Stokes, Navier-Lame, and the semi-discrete eddy current equations.
| Author: | Carsten CarstensenGND, Martin Eigel, Caroline Löbhard, Ronald H. W. HoppeORCiDGND |
|---|---|
| URN: | urn:nbn:de:bvb:384-opus4-11819 |
| Frontdoor URL | https://opus.bibliothek.uni-augsburg.de/opus4/1450 |
| Series (Serial Number): | Preprints des Instituts für Mathematik der Universität Augsburg (2010-13) |
| Type: | Preprint |
| Language: | English |
| Date of Publication (online): | 2010/10/12 |
| Publishing Institution: | Universität Augsburg |
| Contributing Corporation: | Humboldt Universität zu Berlin, Yonsei University Seoul, University of Houston |
| Release Date: | 2010/10/12 |
| Tag: | adaptive algorithms; finite element method; residual estimators; unified a posteriori error analysis |
| GND-Keyword: | Partielle Differentialgleichung; Finite-Elemente-Methode; A-posteriori-Abschätzung; Fehleranalyse |
| Institutes: | Mathematisch-Naturwissenschaftlich-Technische Fakultät |
| Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik | |
| Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik / Lehrstuhl für Numerische Mathematik | |
| Dewey Decimal Classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
| Licence (German): |  Deutsches Urheberrecht |
