Linear convergence of an adaptive finite element method for the p-Laplacian equation
- We study an adaptive finite element method for the p-Laplacian like PDE's using piecewise linear, continuous functions. The error is measured by means of the quasi-norm of Barrett and Liu. We provide residual based error estimators without a gap between the upper and lower bound. We show linear convergence of the algorithm which is similar to the one of Morin, Nochetto, and Siebert. All results are obtained without extra marking for the oscillation.
| Author: | Lars Diening, Christian Kreuzer |
|---|---|
| URN: | urn:nbn:de:bvb:384-opus4-4439 |
| Frontdoor URL | https://opus.bibliothek.uni-augsburg.de/opus4/549 |
| Series (Serial Number): | Preprints des Instituts für Mathematik der Universität Augsburg (2007-24) |
| Type: | Preprint |
| Language: | English |
| Publishing Institution: | Universität Augsburg |
| Contributing Corporation: | Landesstiftung Baden-Württemberg, Project C.1 of the DFG-Research-Unit "Nonlinear Partial Differential Equations" Generalized Newtonian fluid |
| Release Date: | 2007/07/04 |
| Tag: | Nichtlineare partielle Differentialgleichung Linear Convergence |
| GND-Keyword: | A-posteriori-Abschätzung; Adaptives Verfahren; Finite-Elemente-Methode; Elliptische Differentialgleichung |
| Institutes: | Mathematisch-Naturwissenschaftlich-Technische Fakultät |
| Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik | |
| Dewey Decimal Classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
