Discontinuous Petrov–Galerkin Approximation of Eigenvalue Problems

Fleurianne Bertrand, Daniele Boffi, Henrik Schneider

Research output: Contribution to journalArticlepeer-review

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 (US)
JournalComputational Methods in Applied Mathematics
DOIs
StatePublished - May 26 2022

ASJC Scopus subject areas

  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics

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