A meshless Galerkin method for Dirichlet problems using radial basis functions

被引：20

作者：

Duan, Yong ^{[1
]}

Tan, Yong-Ji

机构：

[1] Univ Elect Sci & Technol China, Sch Appl Math, Chengdu 610054, Peoples R China

[2] Fudan Univ, Inst Math, Shanghai 200433, Peoples R China

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2006年 / 196卷 / 02期

关键词：

radial basis functions; Lagrange multipliers; penalty method; Galerkin approximation; meshless;

D O I：

10.1016/j.cam.2005.09.018

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, a numerical method is given for partial differential equations, which combines the use of Lagrange multipliers with radial basis functions. It is a new method to deal with difficulties that arise in the Galerkin radial basis function approximation applied to Dirichlet (also mixed) boundary value problems. Convergence analysis results are given. Several examples show the efficiency of the method using TPS or Sobolev splines. (c) 2005 Elsevier B.V. All rights reserved.

引用

页码：394 / 401

页数：8

共 20 条

[11]

HON YC, 2000, INT J APPL MATH, V4, P81

[12] BOUNDARY SUBSPACES FOR THE FINITE-ELEMENT METHOD WITH LAGRANGE MULTIPLIERS [J].

PITKARANTA, J .

NUMERISCHE MATHEMATIK, 1979, 33 (03) :273-289

[13]

PITKARANTA J, 1981, MATH COMPUT, V37, P515

[14]

PITKARANTA J, 1979, MATH COMPUT, V35, P1113

[15] Improved error bounds for scattered data interpolation by radial basis functions [J].

Schaback, R .

MATHEMATICS OF COMPUTATION, 1999, 68 (225) :201-216

[16]

Schaback R., 1995, Advances in Computational Mathematics, V3, P251, DOI 10.1007/BF02432002

[17] ON SOME TECHNIQUES FOR APPROXIMATING BOUNDARY-CONDITIONS IN THE FINITE-ELEMENT METHOD [J].

STENBERG, R .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 1995, 63 (1-3) :139-148

[18] Error estimates for interpolation by compactly supported radial basis functions of minimal degree [J].

Wendland, H .

JOURNAL OF APPROXIMATION THEORY, 1998, 93 (02) :258-272

[19] Meshless Galerkin methods using radial basis functions [J].

Wendland, H .

MATHEMATICS OF COMPUTATION, 1999, 68 (228) :1521-1531

[20]

Wu Z., 1995, Adv. Comput. Math, V4, P283, DOI [DOI 10.1007/BF03177517, 10.1007/BF03177517]

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