An adaptive finite element method with asymptotic saturation for eigenvalue problems

C. Carstensen; J. Gedicke; V. Mehrmann; A. Międlar

doi:10.1007/s00211-014-0624-2

An adaptive finite element method with asymptotic saturation for eigenvalue problems

C. Carstensen, J. Gedicke, V. Mehrmann, A. Międlar

Research output: Contribution to journal › Article › peer-review

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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.

Original language	English (US)
Pages (from-to)	615-634
Number of pages	20
Journal	Numerische Mathematik
Volume	128
Issue number	4
DOIs	https://doi.org/10.1007/s00211-014-0624-2
State	Published - Dec 2014
Externally published	Yes

Bibliographical note

Funding Information:
Supported by the DFG Research Center MATHEON “Mathematics for key technologies”, and the DFG graduate school BMS “Berlin Mathematical School” in Berlin.

Publisher Copyright:
© 2014, Springer-Verlag Berlin Heidelberg.

Keywords

65N15
65N25
65N30

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doi = "10.1007/s00211-014-0624-2",

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AU - Gedicke, J.

AU - Mehrmann, V.

AU - Międlar, A.

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N2 - 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.

AB - 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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An adaptive finite element method with asymptotic saturation for eigenvalue problems

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