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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The authors would like to thank the anonymous referees for their valuable comments and suggestions.
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Supported by the DFG Research Center MATHEON “Mathematics for key technologies”, and the DFG graduate school BMS “Berlin Mathematical School” in Berlin.
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Carstensen, C., Gedicke, J., Mehrmann, V. et al. An adaptive finite element method with asymptotic saturation for eigenvalue problems. Numer. Math. 128, 615–634 (2014). https://doi.org/10.1007/s00211-014-0624-2
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DOI: https://doi.org/10.1007/s00211-014-0624-2