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A Story on Adaptive Finite Element Computations for Elliptic Eigenvalue Problems

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Numerical Algebra, Matrix Theory, Differential-Algebraic Equations and Control Theory

Abstract

We briefly survey the recent developments in adaptive finite element approximations of eigenvalue problems arising from elliptic, second-order, selfadjoint partial differential equations (PDEs). The main goal of this paper is to present the variety of subjects and corresponding results contributing to this very complex and broad area of research, and to provide a reader with a relevant sources of information for further investigations.

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Albert Pike

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Acknowledgements

The author would like to thank Federico Poloni for careful reading of the paper and providing valuable comments. The work of the author has been supported by the DFG Research Fellowship under the DFG GEPRIS Project Adaptive methods for nonlinear eigenvalue problems with parameters and Chair of Numerical Algorithms and High-Performance Computing, Mathematics Institute of Computational Science and Engineering (MATHICSE), École Polytechnique Fédérale de Lausanne, Switzerland.

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  1. ANCHP – MATHICSE, École Polytechnique Fédérale de Lausanne, Bâtiment MA, Station 8, CH-1015, Lausanne, Switzerland

    Agnieszka Międlar

  2. Institut für Mathematik, Technische Universität Berlin, Sekretariat MA 4-5, Straße des 17. Juni 136, D-10623, Berlin, Germany

    Agnieszka Międlar

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  1. Agnieszka Międlar
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  1. Max Planck Institute for Dynamics of Complex Technical Systems, Magdeburg, Germany

    Peter Benner

  2. Carl-Friedrich-Gauß Fakultät, TU Braunschweig, Institute Computational Mathematics, Braunschweig, Germany

    Matthias Bollhöfer

  3. MATHICSE, École Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland

    Daniel Kressner

  4. Institute of Mathematics, T U Berlin, Berlin, Germany

    Christian Mehl

  5. Institute of Mathematics, University of Augsburg, Augsburg, Germany

    Tatjana Stykel

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Międlar, A. (2015). A Story on Adaptive Finite Element Computations for Elliptic Eigenvalue Problems. In: Benner, P., Bollhöfer, M., Kressner, D., Mehl, C., Stykel, T. (eds) Numerical Algebra, Matrix Theory, Differential-Algebraic Equations and Control Theory. Springer, Cham. https://doi.org/10.1007/978-3-319-15260-8_9

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