OPTIMAL QUADRATIC NITSCHE EXTENDED FINITE ELEMENT METHOD FOR INTERFACE PROBLEM OF DIFFUSION EQUATION  

作　　者：Fei Wang Shuo Zhang 

机构地区：[1]School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an 710049, China [2]Department of Mathematics, Pennsylvania State University, University Park, PA 16802, USA. [3]LSEC, ICMSEC, NCMIS, Academy of Mathematics and System Sciences Chinese Academy of Sciences, Beijing 100190, China.

出　　处：《Journal of Computational Mathematics》2018年第5期693-717,共25页计算数学（英文）

基　　金：The first author is partially supported by the U.S. Department of Energy, Office of Science, Office of Advanced Scientific Computing Research as part of the Collaboratory on Mathematics for Mesoscopic Modeling of Materials under Award Number DE-SC-0009249, and the Key Program of National Natural Science Foundation of China with Grant No. 91430215. The second author is supported by State Key Laboratory of Scientific and Engineering Computing （LSEC）, National Center for Mathematics and Interdisciplinary Sciences of Chinese Academy of Sciences （NCMIS）, and National Natural Science Foundation of China with Grant No. 11471026; he is thankful to the Center for Computational Mathematics and Applications, the Pennsylvania State University, where he worked on this manuscript as a visiting scholar. The authors are grateful to Professor Jinchao Xu, Dr. Yuanming Xiao and Dr. Maximilian Metti for their valuable suggestions and discussions, to Professor Haijun Wu for his valuable help on preparing the numerical example, and to the anonymous referee for the valuable comments and suggestion which lead to improvements of the paper.

摘　　要：In this paper, we study Nitsche extended finite element method （XFEM） for the inter- face problem of a two dimensional diffusion equation. Specifically, we study the quadratic XFEM scheme on some shape-regular family of grids and prove the optimal convergence rate of the scheme with respect to the mesh size. Main efforts are devoted onto classifying the cases of intersection between the elements and the interface and prove a weighted trace inequality for the extended finite element functions needed, and the general framework of analysing XFEM c^n be implemented then.In this paper, we study Nitsche extended finite element method （XFEM） for the inter- face problem of a two dimensional diffusion equation. Specifically, we study the quadratic XFEM scheme on some shape-regular family of grids and prove the optimal convergence rate of the scheme with respect to the mesh size. Main efforts are devoted onto classifying the cases of intersection between the elements and the interface and prove a weighted trace inequality for the extended finite element functions needed, and the general framework of analysing XFEM c^n be implemented then.

关 键 词：Interface problems Extended finite element methods Error estimates Nitsche＇s scheme Quadratic element. 

分 类 号：TP334.7[自动化与计算机技术—计算机系统结构] TM561.506[自动化与计算机技术—计算机科学与技术]