Volume 10, Issue 2
Superconvergence Analysis of Bilinear Finite Element for the Nonlinear Schrodinger Equation on the Rectangular Mesh

Zhikun Tian ,  Yanping Chen and Jianyun Wang

10.4208/aamm.OA-2017-0156

Adv. Appl. Math. Mech., 10 (2018), pp. 468-484

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  • Abstract

In this paper, we investigate the superconvergence property of a timedependent nonlinear Schrodinger equation with the bilinear finite element method on the rectangular mesh. We prove the superclose error estimate in H1-norm with order O(h2) between the approximated solution and the elliptic projection of the exact solution. Moreover, we obtain the global superconvergence result in H1-norm with order O(h2) by the interpolation post-processing operator.

  • History

Published online: 2018-10

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