Finite element method for solving problems with singular solutions

被引：28
|
作者：
Babuska, I
Andersson, B
Guo, B
Melenk, JM
Oh, HS
机构：
[1] UNIV MARYLAND,INST PHYS SCI & TECHNOL,COLLEGE PK,MD 20742
[2] AERONAUT RES INST SWEDEN,S-16111 BROMA,SWEDEN
[3] UNIV MANITOBA,DEPT APPL MATH,WINNIPEG,MB R3T 2N2,CANADA
[4] UNIV N CAROLINA,DEPT MATH,CHARLOTTE,NC 28223
来源：
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 1996年 / 74卷 / 1-2期
基金：
美国国家科学基金会;
关键词：
finite elements; singular solution; hp version of FEM;
D O I：
10.1016/0377-0427(96)00017-9
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Numerical treatment of the elliptic boundary value problem with nonsmooth solution by the finite element method is discussed. The nonsmoothness could have its origin in the unsmooth boundary or the differential equation. This paper, which is a survey of the recent results, elaborates among others on the method of auxiliary mapping, the partition of unity finite element method and the hp version of FEM in three-dimensions. Numerical examples illustrate mathematical results.
引用
收藏
页码：51 / 70
页数：20
相关论文
共 50 条
  • [1] A finite element method for solving singular boundary-value problems
    Yakovlev M.N.
    Journal of Mathematical Sciences, 2008, 150 (2) : 1998 - 2004
  • [2] Fractal finite element method for singular problems
    Su, RKL
    Sun, HY
    Yong, Z
    COMPUTATIONAL MECHANICS, VOLS 1 AND 2, PROCEEDINGS: NEW FRONTIERS FOR THE NEW MILLENNIUM, 2001, : 655 - 660
  • [3] On the finite element method for elliptic problems with degenerate and singular coefficients
    Arroyo, Daniel
    Bespalov, Alexei
    Heuer, Norbert
    MATHEMATICS OF COMPUTATION, 2007, 76 (258) : 509 - 537
  • [4] Neural network method for solving elastoplastic finite element problems
    任小强
    陈务军
    董石麟
    王锋
    Journal of Zhejiang University Science A(Science in Engineering), 2006, (03) : 378 - 382
  • [5] An iterative method for solving finite element model updating problems
    Yuan, Yongxin
    Liu, Hao
    APPLIED MATHEMATICAL MODELLING, 2011, 35 (02) : 848 - 858
  • [6] THE PERTURBATION FINITE ELEMENT METHOD FOR SOLVING PROBLEMS WITH NONLINEAR MATERIALS
    谢志成
    王瑞五
    杨学忠
    钱振东
    AppliedMathematicsandMechanics(EnglishEdition), 1983, (01) : 127 - 140
  • [7] Finite element method for solving geodetic boundary value problems
    Faskova, Zuzana
    Cunderlik, Robert
    Mikula, Karol
    JOURNAL OF GEODESY, 2010, 84 (02) : 135 - 144
  • [8] The polygonal finite element method for solving heat conduction problems
    Wu, Cheng-Tao
    Wu, Shao-Wei
    Niu, Rui-Ping
    Jiang, Chen
    Liu, G. R.
    ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS, 2023, 155 : 935 - 947
  • [9] Neural network method for solving elastoplastic finite element problems
    Ren X.-Q.
    Chen W.-J.
    Dong S.-L.
    Wang F.
    Journal of Zhejiang University: Science, 2006, 7 (03): : 378 - 382
  • [10] Finite element method for solving geodetic boundary value problems
    Zuzana Fašková
    Róbert Čunderlík
    Karol Mikula
    Journal of Geodesy, 2010, 84 : 135 - 144
12345