Finite element approximations of conformal mappings

被引：6

作者：

Tsuchiya, T ^{[1
]}

机构：

[1] Ehime Univ, Fac Sci, Dept Math Sci, Matsuyama, Ehime 7908577, Japan

来源：

NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION | 2001年 / 22卷 / 3-4期

关键词：

conformal mappings; finite elements; variational principle;

D O I：

10.1081/NFA-100105111

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, finite element approximations of conformal mappings defined on the unit disk to Jordan domains are considered. Three types of the normalization conditions are dealt with. In each case, convergence of the finite element conformal mappings to the exact conformal mappings is proved. Several numerical examples are given.

引用

页码：419 / 440

页数：22

共 12 条

[1] Chen XJ, 2000, J OPER RES SOC JPN, V43, P32, DOI 10.1016/S0453-4514(00)88750-5
[2] Ciarlet P. G., 1973, Computer Methods in Applied Mechanics and Engineering, V2, P17, DOI 10.1016/0045-7825(73)90019-4
[3] CIARLET P. G., 1978, The Finite Element Method for Elliptic Problems
[4] Courant Richard, 1950, Dirichlet's Principle, Conformal Mapping, and Minimal Surfaces
[5] Dierkes U, 1992, Minimal Surfaces, VI
[6] SUPERCONVERGENCE PHENOMENON IN THE FINITE-ELEMENT METHOD ARISING FROM AVERAGING GRADIENTS
KRIZEK, M
NEITTAANMAKI, P
[J]. NUMERISCHE MATHEMATIK, 1984, 45 (01) : 105 - 116
[7] ON A GLOBAL SUPERCONVERGENCE OF THE GRADIENT OF LINEAR TRIANGULAR ELEMENTS
KRIZEK, M
NEITTAANMAKI, P
[J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 1987, 18 (02) : 221 - 233
[8] WEAK DISCRETE MAXIMUM PRINCIPLE AND STABILITY OF THE FINITE-ELEMENT METHOD IN L-INFINITY ON PLANE POLYGONAL DOMAINS .1.
SCHATZ, AH
[J]. MATHEMATICS OF COMPUTATION, 1980, 34 (149) : 77 - 91
[9] TSUCHIYA T, 1990, MATH COMPUT, V54, P131, DOI 10.1090/S0025-5718-1990-0993934-2
[10] TSUCHIYA T, 1987, MATH COMPUT, V49, P157, DOI 10.1090/S0025-5718-1987-0890259-0

← 1 2 →