hpfem/esco2012-boa

Switch branches/tags
Nothing to show
Fetching contributors…
Cannot retrieve contributors at this time
34 lines (27 sloc) 1.52 KB
 \title{An Optimal Eigenvalue Solver} \tocauthor{J. Gedicke} \author{} \institute{} \maketitle \begin{center} {\large Joscha Gedicke}\\ Dipl.-Math.\\ {\tt gedicke@math.hu-berlin.de} \end{center} \section*{Abstract} This talk presents the optimal computational complexity of a combined adaptive finite element method (AFEM) with an iterative algebraic eigenvalue solver for a simple symmetric model problem. The analysis is based on a direct approach for eigenvalue problems and allows the use of higher order conforming finite element spaces with fixed polynomial degree. First the quasi-optimal convergence for the eigenvalue problem under the usual assumption that the sub-problems are solved exactly is shown. As for the source problem the convergence analysis for the quasi error does not need the inner node property. These results are relaxed to the inexact approximations of some iterative eigenvalue solver and thus lead to a combined AFEM and iterative eigenvalue solver algorithm. The proposed optimal algorithm involves a proper termination criterion for the iterative algebraic eigenvalue solver and does not need any coarsening. Numerical examples show optimal computational complexity. This contribution is joint work with Carsten Carstensen (HU Berlin, Germany). \bibliographystyle{plain} \begin{thebibliography}{10} \bibitem{CG_OptimalAFEMES} {\sc C. Carstensen and J. Gedicke}. {An Adaptive Finite Element Eigenvalue Solver of Quasi-Optimal Computational Complexity}. MATHEON Preprint 662 (2009), TU Berlin. \end{thebibliography}