Solving Elliptic Eigenproblems with Adaptive Multimesh hp-FEM

Giani, S.; Solin, P.

Abstract

This paper proposes a novel adaptive higher-order nite element (hp-FEM) method for solving elliptic eigenvalue problems, where n eigenpairs are calculated simultaneously, but on individual higher-order nite element meshes. The meshes are automatically hp-rened independently of each other, with the goal to use an optimal mesh sequence for each eigenfunction. The method and the adaptive algorithm are described in detail. Numerical examples clearly demonstrate the superiority of the novel method over the standard approach where all eigenfunctions are approximated on the same nite element mesh.

Citation

Giani, S., & Solin, P. (2021). Solving Elliptic Eigenproblems with Adaptive Multimesh hp-FEM. Journal of Computational and Applied Mathematics, 394, Article 113528. https://doi.org/10.1016/j.cam.2021.113528

• Journal Article Type: Article
• Acceptance Date: Feb 24, 2021
• Online Publication Date: Mar 13, 2021
• Publication Date: Oct 1, 2021
• Deposit Date: Feb 25, 2021
• Publicly Available Date: Mar 13, 2022
• Journal: Journal of Computational and Applied Mathematics
• Print ISSN: 0377-0427
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 394
• Article Number: 113528
• DOI: https://doi.org/10.1016/j.cam.2021.113528