Finite Element Approximation of the Modified Maxwell's Stekloff Eigenvalues
Abstract
The modified Maxwell's Stekloff eigenvalue problem arises recently from the inverse electromagnetic scattering theory for inhomogeneous media. This paper contains a rigorous analysis of both the eigenvalue problem and the associated source problem on Lipschitz polyhedra. A new finite element method is proposed to compute Stekloff eigenvalues. By applying the Babuska-Osborn theory, we prove an error estimate without additional regularity assumptions. Numerical results are presented for validation.
- Publication:
-
arXiv e-prints
- Pub Date:
- April 2020
- DOI:
- 10.48550/arXiv.2004.04588
- arXiv:
- arXiv:2004.04588
- Bibcode:
- 2020arXiv200404588G
- Keywords:
-
- Mathematics - Numerical Analysis;
- 65N25;
- 65N30;
- 35Q61