Two-grid methods for semi-linear elliptic interface problems by immersed finite element methods  

作　　者：Yang WANG Yanping CHEN Yunqing HUANG Ying LIU 

机构地区：[1]School of Mathematics and Computational Science,Xiangtan University,Xiangtan 411105,Hunan Province,China [2]School of Mathematical Sciences,South China Normal University,Guangzhou 510631,China [3]College of Science,Hunan Agricultural University,Changsha 410128,China

出　　处：《Applied Mathematics and Mechanics(English Edition)》2019年第11期1657-1676,共20页应用数学和力学（英文版）

基　　金：Project supported by the National Natural Science Foundation of China(Nos.11671157 and11826212)

摘　　要：In this paper,two-grid immersed finite element (IFE) algorithms are proposed and analyzed for semi-linear interface problems with discontinuous diffusion coefficients in two dimension.Because of the advantages of finite element (FE) formulation and the simple structure of Cartesian grids,the IFE discretization is used in this paper.Two-grid schemes are formulated to linearize the FE equations.It is theoretically and numerically illustrated that the coarse space can be selected as coarse as H =O(h^1/4)(or H =O(h^1/8)),and the asymptotically optimal approximation can be achieved as the nonlinear schemes.As a result,we can settle a great majority of nonlinear equations as easy as linearized problems.In order to estimate the present two-grid algorithms,we derive the optimal error estimates of the IFE solution in the L^p norm.Numerical experiments are given to verify the theorems and indicate that the present two-grid algorithms can greatly improve the computing efficiency.In this paper, two-grid immersed finite element（IFE） algorithms are proposed and analyzed for semi-linear interface problems with discontinuous diffusion coefficients in two dimension. Because of the advantages of finite element（FE） formulation and the simple structure of Cartesian grids, the IFE discretization is used in this paper. Two-grid schemes are formulated to linearize the FE equations. It is theoretically and numerically illustrated that the coarse space can be selected as coarse asH= O(h1/4)(orH=O(h1/8)), and the asymptotically optimal approximation can be achieved as the nonlinear schemes. As a result, we can settle a great majority of nonlinear equations as easy as linearized problems. In order to estimate the present two-grid algorithms, we derive the optimal error estimates of the IFE solution in theL pnorm. Numerical experiments are given to verify the theorems and indicate that the present two-grid algorithms can greatly improve the computing efficiency.

关 键 词：two-grid METHOD INTERFACE PROBLEM FINITE ELEMENT METHOD immersed INTERFACE 

分 类 号：O241[理学—计算数学]