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An adaptive finite element method with asymptotic saturation for eigenvalue problems |
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| Authors: | C Carstensen J Gedicke V Mehrmann A Międlar |
| Institution: | 1. Humboldt-Universit?t zu Berlin, Unter den Linden 6, 10099?, Berlin, Germany 2. Department of Computational Science and Engineering, Yonsei University, Seoul, 120–749, Korea 3. Department of Mathematics and Center for Computation and Technology, Louisiana State University, Baton Rouge, LA, 70803, USA 4. Institut für Mathematik, MA 4-5 TU Berlin, Strasse des 17. Juni 136, 10623?, Berlin, Germany |
| Abstract: | This paper discusses adaptive finite element methods for the solution of elliptic eigenvalue problems associated with partial differential operators. An adaptive method based on nodal-patch refinement leads to an asymptotic error reduction property for the computed sequence of simple eigenvalues and eigenfunctions. This justifies the use of the proven saturation property for a class of reliable and efficient hierarchical a posteriori error estimators. Numerical experiments confirm that the saturation property is present even for very coarse meshes for many examples; in other cases the smallness assumption on the initial mesh may be severe. |
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