Discontinuous Petrov-Galerkin Approximation of Eigenvalue Problems

Fleurianne Bertrand, Daniele Boffi*, Henrik Schneider

*Corresponding author for this work

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Abstract

In this paper, the discontinuous Petrov-Galerkin approximation of the Laplace eigenvalue problem is discussed. We consider in particular the primal and ultraweak formulations of the problem and prove the convergence together with a priori error estimates. Moreover, we propose two possible error estimators and perform the corresponding a posteriori error analysis. The theoretical results are confirmed numerically, and it is shown that the error estimators can be used to design an optimally convergent adaptive scheme.

Original languageEnglish
JournalComputational Methods in Applied Mathematics
Early online date26 May 2022
DOIs
Publication statusE-pub ahead of print/First online - 26 May 2022

Keywords

  • DPG Methods
  • Eigenvalue Problems

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