ERROR ANALYSIS OF A CONFORMING FINITE ELEMENT METHOD FOR THE MODIFIED ELECTROMAGNETIC TRANSMISSION EIGENVALUE PROBLEM

Document Type

Article

Publication Date

4-2026

Department

Department of Mathematical Sciences

Abstract

The modified electromagnetic transmission eigenvalue problem (METEP) arises from the inverse scattering theory and can be used to detect changes of the material properties in nondestructive testing. This paper proposes and analyzes a conforming edge element method for the METEP. We establish a rigorous error analysis of the numerical eigenpairs by proving the uniform convergence of the discrete operator. In particular, as the problem contains two second order equations and is indefinite, we introduce auxiliary problems and show that they satisfy \scrT -coercivity, based on which we prove the existence of both the continuous and discrete solution operators to the source problem. We then prove the uniform convergence of the discrete solution operator by reformulating the continuous and discrete solution operators. Optimal error estimates are obtained by investigating the adjoint problems and using the spectral approximation theory for compact operators. The theory is validated by numerical examples with various coefficients for different domains in both two and three dimensions.

Publication Title

SIAM Journal on Numerical Analysis

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