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

0570477 - MÚ 2024 RIV NL eng J - Journal Article
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
R&D Projects: GA ČR(CZ) GA20-01074S
Institutional support: RVO:67985840
Keywords : Laplace eigenvalue problem * guaranteed error estimation * eigenfunction approximation * finite element method
OECD category: Pure mathematics
Impact factor: 2.4, year: 2022
Method of publishing: Limited access
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.
Permanent Link: https://hdl.handle.net/11104/0341777