Finite element method for a nonsmooth elliptic equation

被引：9
|
作者：
Chang, Lili [1 ]
Gong, Wei [2 ]
Yan, Ningning [1 ]
机构：
[1] Chinese Acad Sci, Inst Syst Sci, State Key Lab Sci & Engn Comp, Acad Math & Syst Sci, Beijing 100190, Peoples R China
[2] Chinese Acad Sci, Inst Computat Math, State Key Lab Sci & Engn Comp, Acad Math & Syst Sci, Beijing 100190, Peoples R China
来源：
FRONTIERS OF MATHEMATICS IN CHINA | 2010年 / 5卷 / 02期
基金：
中国国家自然科学基金;
关键词：
Finite element method; nonsmooth elliptic equation; a priori error estimate; a posteriori error estimate; superconvergence analysis; active set method;
D O I：
10.1007/s11464-010-0001-0
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we study the finite element method for a non-smooth elliptic equation. Error analysis is presented, including a priori and a posteriori error estimates as well as superconvergence analysis. We also propose two algorithms for solving the underlying equation. Numerical experiments are employed to confirm our error estimations and the efficiency of our algorithms.
引用
收藏
页码：191 / 209
页数：19
相关论文
共 50 条
  • [1] Finite element method for a nonsmooth elliptic equation
    Lili Chang
    Wei Gong
    Ningning Yan
    Frontiers of Mathematics in China, 2010, 5 : 191 - 209
  • [2] THE FINITE-ELEMENT METHOD FOR A DEGENERATE ELLIPTIC EQUATION
    FRENCH, DA
    SIAM JOURNAL ON NUMERICAL ANALYSIS, 1987, 24 (04) : 788 - 815
  • [3] CONVERGENCE OF THE HETEROGENEOUS MULTISCALE FINITE ELEMENT METHOD FOR ELLIPTIC PROBLEMS WITH NONSMOOTH MICROSTRUCTURES
    Du, Rui
    Ming, Pingbing
    MULTISCALE MODELING & SIMULATION, 2010, 8 (05): : 1770 - 1783
  • [4] A Rectangular Finite Volume Element Method for a Semilinear Elliptic Equation
    Zhiguang Xiong
    Yanping Chen
    Journal of Scientific Computing, 2008, 36 : 177 - 191
  • [5] Convergence of the finite element method for an elliptic equation with strong degeneration
    Urev M.V.
    Journal of Applied and Industrial Mathematics, 2014, 8 (03) : 411 - 421
  • [6] Finite element method for fourth order nonstationary elliptic equation
    Dai, Peiliang
    Dai, Jiazun
    Nanjing Hangkong Hangtian Daxue Xuebao/Journal of Nanjing University of Aeronautics and Astronautics, 2002, 34 (01):
  • [7] A rectangular finite volume element method for a semilinear elliptic equation
    Xiong, Zhiguang
    Chen, Yanping
    JOURNAL OF SCIENTIFIC COMPUTING, 2008, 36 (02) : 177 - 191
  • [8] A TRIANGULAR FINITE VOLUME ELEMENT METHOD FOR A SEMILINEAR ELLIPTIC EQUATION
    Xiong, Zhiguang
    Chen, Yanping
    JOURNAL OF COMPUTATIONAL MATHEMATICS, 2014, 32 (02) : 152 - 168
  • [9] An adaptive finite element method for a linear elliptic equation with variable coefficients
    Dörfler, W
    Wilderotter, O
    ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK, 2000, 80 (07): : 481 - 491
  • [10] Modified intrinsic extended finite element method for elliptic equation with interfaces
    Jianping Zhao
    Yanren Hou
    Lina Song
    Journal of Engineering Mathematics, 2016, 97 : 147 - 159
12345