An asymptotically exact a posteriori error estimator for non-selfadjoint Steklov eigenvalue problem

This paper aims to introduce an asymptotically exact a posteriori error estimator for non-selfadjoint Steklov eigenvalue problem arising from inverse scattering by using the complementary technique, which provides an asymptotically exact estimate for eigenpair of non-selfadjoint Steklov eigenvalue problem. Besides, as its applications, we design a novel cascadic adaptive method for non-selfadjoint Steklov eigenvalue problem based on the asymptotically exact estimate. In our novel algorithm, we will transform the non-selfadjoint Steklov eigenvalue problem into some boundary value problems on the adaptive space sequence and some non-selfadjoint Steklov eigenvalue problem on a low dimensional finite element space. The involved boundary value problems are solved by executing some smoothing steps which is the key point of cascadic algorithm. The mesh refinement strategy and the number of smoothing steps for the cascadic adaptive method will be controlled by the proposed asymptotically exact a posteriori error estimator. (C) 2020 IMACS. Published by Elsevier B.V. All rights reserved.