Finite Element Approximation of the Modified Maxwell's Stekloff Eigenvalues

2020/04/09 by Gong, Bo, Sun, Jiguang, Wu, Xinming
#35Q61 #65N25 #65N30 #FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.2004.04588

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.

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