Projection-based guaranteed L2 error bounds for finite element approximations of Laplace eigenfunctions

0570477 - MÚ 2024 RIV NL eng J - Článek v odborném periodiku
Liu, X. - Vejchodský, Tomáš
Projection-based guaranteed L2 error bounds for finite element approximations of Laplace eigenfunctions.
Journal of Computational and Applied Mathematics. Roč. 429, September (2023), č. článku 115164. ISSN 0377-0427. E-ISSN 1879-1778
Grant CEP: GA ČR(CZ) GA20-01074S
Institucionální podpora: RVO:67985840
Klíčová slova: Laplace eigenvalue problem * guaranteed error estimation * eigenfunction approximation * finite element method
Obor OECD: Pure mathematics
Impakt faktor: 2.4, rok: 2022
Způsob publikování: Omezený přístup
https://doi.org/10.1016/j.cam.2023.115164

For conforming finite element approximations of the Laplacian eigenfunctions, a fully computable guaranteed error bound in the L2 norm sense is proposed. The bound is based on the a priori error estimate for the Galerkin projection of the conforming finite element method, and has an optimal speed of convergence for the eigenfunctions with the worst regularity. The resulting error estimate bounds the distance of spaces of exact and approximate eigenfunctions and, hence, is robust even in the case of multiple and tightly clustered eigenvalues. The accuracy of the proposed bound is illustrated by numerical examples.
Trvalý link: https://hdl.handle.net/11104/0341777