Extrapolation and superconvergence of the Steklov eigenvalue problem

On the basis of a transform lemma, an asymptotic expansion of the bilinear finite element is derived over graded meshes for the Steklov eigenvalue problem, such that the Richardson extrapolation can be applied to increase the accuracy of the approximation, from which the approximation of O(h3.5) is obtained. In addition, by means of the Rayleigh quotient acceleration technique and an interpolation postprocessing method, the superconvergence of the bilinear finite element is presented over graded meshes for the Steklov eigenvalue problem, and the approximation of O(h3) is gained. Finally, numerical experiments are provided to demonstrate the theoretical results.