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This paper proposes and analyzes an a posteriori error estimator for thefinite element multi-scale discretization approximation of the Stekloveigenvalue problem. Based on the a posteriori error estimates, an adaptivealgorithm of shifted inverse iteration type is designed. Finally, numericalexperiments comparing the performances of three kinds of different adaptivealgorithms are provided, which illustrate the efficiency of the adaptivealgorithm proposed here.

An adaptive algorithm based on the shifted inverse iteration for the Steklov eigenvalue problem