An Adaptive Conforming Mixed Method for the Modified Transmission Eigenvalue Problem for Absorbing Medium

Abstract

In this paper, we study the a posteriori error estimates of the conforming mixed method for the modified transmission eigenvalue problem proposed by Cogar et al. (Inverse Problems 33: 055010, 2017). We give the a posteriori error estimator of the approximate eigenpair, prove the reliability and efficiency of the estimator for the approximate eigenfunction, and present the reliability of the estimator for the approximate eigenvalue. We also implement adaptive computation and exhibit the numerical experiments which show that the approximate eigenvalues obtained by the adaptive computation reach the optimal convergence order.

Keywords

Modified transmission eigenvalues / Conforming mixed method / A priori error estimates / A posteriori error estimates / Absorbing media / Adaptive method / 65N25 / 65N30

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Funding

National Natural Science Foundation of China(11561014)

RIGHTS & PERMISSIONS

Shanghai University