| Автор | Dahlke, Stephan |
| Автор | Hochmuth, Reinhard |
| Автор | Urban, Karsten |
| Дата выпуска | 2000 |
| dc.description | Recently, adaptive wavelet strategies for symmetric, positive definite operators have been introduced that were proven to converge. This paper is devoted to the generalization to saddle point problems which are also symmetric, but indefinite. Firstly, we investigate a posteriori error estimates and generalize the known adaptive wavelet strategy to saddle point problems. The convergence of this strategy for elliptic operators essentially relies on the positive definite character of the operator. As an alternative, we introduce an adaptive variant of Uzawa's algorithm and prove its convergence. Secondly, we derive explicit criteria for adaptively refined wavelet spaces in order to fulfill the Ladyshenskaja-Babuška-Brezzi (LBB) condition and to be fully equilibrated. |
| Формат | application.pdf |
| Издатель | EDP Sciences |
| Копирайт | © EDP Sciences, SMAI, 2000 |
| Тема | Adaptive schemes |
| Тема | aposteriori error estimates |
| Тема | multiscale methods |
| Тема | wavelets |
| Тема | saddle point problems |
| Тема | Uzawa's algorithm. |
| Название | Adaptive wavelet methods for saddle point problems |
| Тип | research-article |
| DOI | 10.1051/m2an:2000113 |
| Electronic ISSN | 1290-3841 |
| Print ISSN | 0764-583X |
| Журнал | ESAIM: Mathematical Modelling and Numerical Analysis |
| Том | 34 |
| Первая страница | 1003 |
| Последняя страница | 1022 |
| Аффилиация | Dahlke Stephan; RWTH Aachen, Institut für Geometrie und Praktische Mathematik, Templergraben 55, 52056 Aachen, Germany. (dahlke@igpm.rwth-aachen.de) |
| Аффилиация | Hochmuth Reinhard; FU Berlin, FB Mathematik, Arnimallee 2-6, 14195 Berlin, Germany. (hochmuth@math.fu-berlin.de) |
| Аффилиация | Urban Karsten; RWTH Aachen, Institut für Geometrie und Praktische Mathematik, Templergraben 55, 52056 Aachen, Germany. (urban@igpm.rwth-aachen.de) |
| Выпуск | 5 |
