Pointwise A Posteriori Error Estimates for Monotone Semi-linear Equations
- We derive upper and lower a posteriori estimates for the maximum norm error in finite element solutions of monotone semi-linear equations. The estimates hold for Lagrange elements of any fixed order, non-smooth nonlinearities, and take numerical integration into account. The proof hinges on constructing continuous barrier functions by correcting the discrete solution appropriately, and then applying the continuous maximum principle; no geometric mesh constraints are thus required. Numerical experiments illustrate reliability and efficiency properties of the corresponding estimators and investigate the performance of the resulting adaptive algorithms in terms of the polynomial order and quadrature.
| Author: | Ricardo H. Nochetto, Alfred Schmidt, Kunibert G. SiebertGND, Andreas Veeser |
|---|---|
| URN: | urn:nbn:de:bvb:384-opus4-508 |
| Frontdoor URL | https://opus.bibliothek.uni-augsburg.de/opus4/71 |
| Series (Serial Number): | Preprints des Instituts für Mathematik der Universität Augsburg (2005-01) |
| Type: | Preprint |
| Language: | English |
| Publishing Institution: | Universität Augsburg |
| Release Date: | 2005/07/08 |
| Tag: | a posteriori estimates; semi-linear equations; maximum norm; numerical integration |
| GND-Keyword: | A-posteriori-Abschätzung; Numerische Mathematik |
| Institutes: | Mathematisch-Naturwissenschaftlich-Technische Fakultät |
| Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik | |
| Dewey Decimal Classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
