Discontinuous Petrov–Galerkin Approximation of Eigenvalue Problems

Autor:	Fleurianne Bertrand, Daniele Boffi, Henrik Schneider
Přispěvatelé:	Mathematics of Computational Science, MESA+ Institute
Rok vydání:	2022
Předmět:	Computational Mathematics Numerical Analysis DPG Methods Applied Mathematics Mathematik Eigenvalue problems
Zdroj:	Computational Methods in Applied Mathematics, 23(1), 1-17. De Gruyter
ISSN:	1609-9389 1609-4840
DOI:	10.1515/cmam-2022-0069
Popis:	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.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::59c69c751135239548ba42617b1a74aa https://doi.org/10.1515/cmam-2022-0069 Zobrazit plný text záznamu