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Superconvergence Analysis of Bilinear Finite Element for the Nonlinear Schrödinger Equation on the Rectangular Mesh

Superconvergence Analysis of Bilinear Finite Element for the Nonlinear Schrödinger Equation on the Rectangular Mesh
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Year:    2018

Author:    Zhikun Tian, Yanping Chen, Jianyun Wang

Advances in Applied Mathematics and Mechanics, Vol. 10 (2018), Iss. 2 : pp. 468–484

Abstract

In this paper, we investigate the superconvergence property of a time-dependent nonlinear Schrödinger equation with the bilinear finite element method on the rectangular mesh. We prove the superclose error estimate in $H^1$-norm with order $\mathcal{O}(h^2)$ between the approximated solution and the elliptic projection of the exact solution. Moreover, we obtain the global superconvergence result in $H^1$-norm with order $\mathcal{O}(h^2)$ by the interpolation post-processing operator.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/aamm.OA-2017-0156

Advances in Applied Mathematics and Mechanics, Vol. 10 (2018), Iss. 2 : pp. 468–484

Published online:    2018-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    17

Keywords:    Finite element method nonlinear Schrödinger equation superconvergence interpolation post-processing.

Author Details

Zhikun Tian

Yanping Chen

Jianyun Wang

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