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

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F23%3A00570477" target="_blank" >RIV/67985840:_____/23:00570477 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1016/j.cam.2023.115164" target="_blank" >https://doi.org/10.1016/j.cam.2023.115164</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.cam.2023.115164" target="_blank" >10.1016/j.cam.2023.115164</a>

Result language
angličtina
Original language name
Projection-based guaranteed L2 error bounds for finite element approximations of Laplace eigenfunctions
Original language description
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.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GA20-01074S" target="_blank" >GA20-01074S: Adaptive methods for the numerical solution of partial differential equations: analysis, error estimates and iterative solvers</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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