An Augmented Two-Scale Finite Element Method for Eigenvalue Problems

doi:10.1007/s42967-024-00375-0

Abstract

Abstract: In this paper, an augmented two-scale finite element method is proposed for a class of linear and nonlinear eigenvalue problems on tensor-product domains. Through a correction step, the augmented two-scale finite element solution is obtained by solving an eigenvalue problem on a low-dimensional augmented subspace. Theoretical analysis and numerical experiments show that the augmented two-scale finite element solution achieves the same order of accuracy as the standard finite element solution on a fine grid, but the computational cost required by the former solution is much lower than that demanded by the latter. The augmented two-scale finite element method also improves the approximation accuracy of eigenfunctions in the L²(Ω) norm compared with the two-scale finite element method.

Key words: Two-scale, Finite element, Augmented subspace method, Eigenvalue problem, Partial differential equation

CLC Number:

Xiaoying Dai, Yunyun Du, Fang Liu, Aihui Zhou. An Augmented Two-Scale Finite Element Method for Eigenvalue Problems[J]. Communications on Applied Mathematics and Computation, 2025, 7(2): 663-688.

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