Discontinuous Petrov-Galerkin Approximation of Eigenvalue Problems

Fleurianne Bertrand, Daniele Boffi*, Henrik Schneider

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

1 Citation (Scopus)
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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
Pages (from-to)1-17
JournalComputational Methods in Applied Mathematics
Volume23
Issue number1
Early online date26 May 2022
DOIs
Publication statusPublished - 1 Jan 2023

Keywords

  • DPG Methods
  • Eigenvalue problems

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