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

机译:浸入式有限元法求解半线性椭圆界面问题的两网格方法

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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.

著录项

  • 来源
    《应用数学和力学(英文版)》 |2019年第11期|1657-1676|共20页
  • 作者单位

    School of Mathematics and Computational Science Xiangtan University Xiangtan 411105 Hunan Province China;

    School of Mathematical Sciences South China Normal University Guangzhou 510631 China;

    College of Science Hunan Agricultural University Changsha 410128 China;

  • 收录信息 中国科学引文数据库(CSCD);
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类 数值分析;
  • 关键词

  • 入库时间 2022-08-19 04:31:53
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