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.
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