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Optimal convergence of adaptive FEM for eigenvalue clusters in mixed form


Authors: Daniele Boffi, Dietmar Gallistl, Francesca Gardini and Lucia Gastaldi
Journal: Math. Comp. 86 (2017), 2213-2237
MSC (2010): Primary 65N30, 65N25, 65N50
DOI: https://doi.org/10.1090/mcom/3212
Published electronically: February 13, 2017
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Abstract: It is shown that the $ h$-adaptive mixed finite element method for the discretization of eigenvalue clusters of the Laplace operator produces optimal convergence rates in terms of nonlinear approximation classes. The results are valid for the typical mixed spaces of Raviart-Thomas or Brezzi-Douglas-Marini type with arbitrary fixed polynomial degree in two and three space dimensions.


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Additional Information

Daniele Boffi
Affiliation: Dipartimento di Matematica “F. Casorati”, University of Pavia, Italy
Email: daniele.boffi@unipv.it

Dietmar Gallistl
Affiliation: Institut für Angewandte und Numerische Mathematik, Karlsruher Institut für Technologie, Germany
Email: gallistl@kit.edu

Francesca Gardini
Affiliation: Dipartimento di Matematica “F. Casorati”, University of Pavia, Italy
Email: francesca.gardini@unipv.it

Lucia Gastaldi
Affiliation: DICATAM, University of Brescia, Italy
Email: lucia.gastaldi@unibs.it

DOI: https://doi.org/10.1090/mcom/3212
Keywords: Mixed finite element method, eigenvalue problem, clusters of eigenvalues, adaptive finite element method
Received by editor(s): May 1, 2015
Received by editor(s) in revised form: April 22, 2016
Published electronically: February 13, 2017
Additional Notes: The first author was supported in part by PRIN/MIUR, GNCS/INDAM, and IMATI/CNR, Italy.
The second author gratefully acknowledges the hospitality of the Dipartimento di Matematica “F. Casorati” (University of Pavia) during his stay in September 2014.
The fourth author was supported in part by PRIN/MIUR, GNCS/INDAM, and IMATI/CNR, Italy.
Article copyright: © Copyright 2017 American Mathematical Society