A NONCONFORMING QUADRILATERAL FINITE ELEMENT APPROXIMATION TO NONLINEAR SCHRODINGER EQUATION

doi:10.1016/S0252-9602(17)30024-3

Acta mathematica scientia,Series B ›› 2017, Vol. 37 ›› Issue (3): 584-592.doi: 10.1016/S0252-9602(17)30024-3

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A NONCONFORMING QUADRILATERAL FINITE ELEMENT APPROXIMATION TO NONLINEAR SCHRODINGER EQUATION

Dongyang SHI¹, Xin LIAO², Lele WANG¹

1. School of Mathematics and Statistics, Zhengzhou University, Zhengzhou 450001, China;
2. Department of Mathematics and Physics, Zhengzhou University of Aeronautics, Zhengzhou 450046, China

Received:2015-03-18 Revised:2016-03-17 Online:2017-06-25 Published:2017-06-25
Supported by:
The research was supported by the National Natural Science Foundation of China (11271340,11101381).

Abstract

Abstract: In this article, a nonconforming quadrilateral element (named modified quasiWilson element) is applied to solve the nonlinear schrödinger equation (NLSE). On the basis of a special character of this element, that is, its consistency error is of order O(h³) for broken H¹-norm on arbitrary quadrilateral meshes, which is two order higher than its interpolation error, the optimal order error estimate and superclose property are obtained. Moreover, the global superconvergence result is deduced with the help of interpolation postprocessing technique. Finally, some numerical results are provided to verify the theoretical analysis.

Key words: Nonlinear Schrödinger equation, modified quasi-Wilson element, supercloseness and superconvergence

Dongyang SHI, Xin LIAO, Lele WANG. A NONCONFORMING QUADRILATERAL FINITE ELEMENT APPROXIMATION TO NONLINEAR SCHRODINGER EQUATION[J].Acta mathematica scientia,Series B, 2017, 37(3): 584-592.

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A NONCONFORMING QUADRILATERAL FINITE ELEMENT APPROXIMATION TO NONLINEAR SCHRODINGER EQUATION

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