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
  • [31] Arbitrary order uniformly convergent finite element method for singular perturbation problems
    Li, Jichun
    Numerical Functional Analysis and Optimization, 1999, 20 (07): : 737 - 751
  • [32] Singular Values Decomposition in Inverse Problems Approximated with Finite Element Method.
    Sikora, Jan
    Skoczylas, Jerzy
    Sroka, Jan
    Tobola, Andrzej
    Wincenciak, Stanislaw
    1600, (31):
  • [33] SINGULAR PROBLEMS AND THE GLOBAL ELEMENT METHOD
    HENDRY, JA
    COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 1980, 21 (01) : 1 - 15
  • [34] FINITE ELEMENT METHOD OF SOLVING THE BOUNDARY PROBLEMS IN NONLINEAR PHYSICAL MEDIA.
    Borkowski, Szczepan
    1978, 26 (03): : 183 - 188
  • [35] Advances in the Particle Finite Element Method (PFEM) for Solving Coupled Problems in Engineering
    Onate, E.
    Idelsohn, S. R.
    Celigueta, M. A.
    Rossi, R.
    Marti, J.
    Carbonell, J. M.
    Ryzhakov, P.
    Suarez, B.
    PARTICLE-BASED METHODS: FUNDAMENTALS AND APPLICATIONS, 2011, 25 : 1 - 49
  • [36] FINITE-ELEMENT METHOD - POSSIBILITIES OF ITS USE FOR SOLVING ELECTROTECHNICAL PROBLEMS
    FANELLI, M
    ELETTROTECNICA, 1975, 62 (06): : 513 - 520
  • [37] TOPOLOGY-FINITE-ELEMENT METHOD FOR SOLVING ELECTROMAGNETIC-FIELD PROBLEMS
    SONG, GX
    SHI, HL
    ELECTRONICS LETTERS, 1983, 19 (15) : 572 - 574
  • [38] Multilevel correction adaptive finite element method for solving nonsymmetric eigenvalue problems
    Xu, Fei
    Yue, Meiling
    Zheng, Bin
    ADVANCES IN COMPUTATIONAL MATHEMATICS, 2021, 47 (02)
  • [39] PERTURBATION FINITE ELEMENT METHOD FOR SOLVING GEOMETRICALLY NONLINEAR PROBLEMS OF AXISYMMETRICAL SHELL
    谢志成
    杨学忠
    钱振东
    刘燕
    张立平
    AppliedMathematicsandMechanics(EnglishEdition), 1984, (05) : 1679 - 1691
  • [40] Multilevel correction adaptive finite element method for solving nonsymmetric eigenvalue problems
    Fei Xu
    Meiling Yue
    Bin Zheng
    Advances in Computational Mathematics, 2021, 47
12345