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Adaptive solution of elliptic PDE‐eigenvalue problems.
Author(s) -
Mehrmann Volker,
Międlar Agnieszka
Publication year - 2009
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200910263
Subject(s) - eigenvalues and eigenvectors , discretization , mathematics , solver , divide and conquer eigenvalue algorithm , algebraic number , iterative and incremental development , iterative method , mathematical optimization , mathematical analysis , computer science , physics , software engineering , quantum mechanics
In this paper we introduce a new adaptive algorithm (AFEMLA) for elliptic PDE‐eigenvalue problems. In contrast to other approaches the algebraic eigenvalue problem does not have to be solved to full accuracy. We incorporate the iterative solution of the resulting finite dimensional algebraic eigenvalue problems in the adaptation process in order to balance the cost with the costs for the iterative eigenvalue method. We present error estimates that incorporate the discretization errors, approximation errors in the eigenvalue solver and roundoff errors. (© 2009 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)