A NONCONFORMING QUADRILATERAL FINITE ELEMENT APPROXIMATION TO NONLINEAR SCHRDINGER EQUATION  

作　　者：石东洋 廖歆 王乐乐 

机构地区：[1]School of Mathematics and Statistics, Zhengzhou University, Zhengzhou 450001, China [2]Department of Mathematics and Physics, Zhengzhou University of Aeronautics, Zhengzhou 450046, China

出　　处：《Acta Mathematica Scientia》2017年第3期584-592,共9页数学物理学报（B辑英文版）

基　　金：supported by the National Natural Science Foundation of China(11271340,11101381)

摘　　要：In this article, a nonconforming quadrilateral element （named modified quasi- Wilson element） is applied to solve the nonlinear schrSdinger equation （NLSE）. On the basis of a special character of this element, that is, its consistency error is of order O（ha） for broken Ha-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.In this article, a nonconforming quadrilateral element （named modified quasi- Wilson element） is applied to solve the nonlinear schrSdinger equation （NLSE）. On the basis of a special character of this element, that is, its consistency error is of order O（ha） for broken Ha-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.

关 键 词：Nonlinear SchrSdinger equation modified quasi-Wilson element superclose-ness and supereonvergenee 

分 类 号：O241.82[理学—计算数学]