Superconvergence analysis of bi-k-degree rectangular elements for two-dimensional time-dependent Schrödinger equation
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Superconvergence has been studied for long, and many different numerical methods have been analyzed. This paper is concerned with the problem of superconvergence for a two-dimensional time-dependent linear Schrödinger equation with the finite element method. The error estimate and superconvergence property with order O(hk+1) in the H1 norm are given by using the elliptic projection operator in the semi-discrete scheme. The global superconvergence is derived by the interpolation post-processing technique. The superconvergence result with order O(hk+1 + τ2) in the H1 norm can be obtained in the Crank-Nicolson fully discrete scheme.
Key wordssuperconvergence elliptic projection Schrödinger equation interpolation post-processing
Chinese Library ClassificationO241.82
2010 Mathematics Subject Classification65M12 65M15 65M60
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We would like to thank anonymous referees for their insightful comments that improved this paper.
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