Stable and convergent unsymmetric meshless collocation methods

被引：66

作者：

Ling, Leevan ^{[1
]}

Schaback, Robert ^{[2
]}

机构：

[1] Hong Kong Baptist Univ, Dept Math, Kowloon, Peoples R China

[2] Univ Gottingen, Inst Numer & Angew Math, D-37083 Gottingen, Germany

来源：

SIAM JOURNAL ON NUMERICAL ANALYSIS | 2008年 / 46卷 / 03期

关键词：

Kansa's method; convergence; error bounds; linear optimization;

D O I：

10.1137/06067300X

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In the theoretical part of this paper, we introduce a simplified proof technique for error bounds and convergence of a variation of Kansa's well-known unsymmetric meshless collocation method. For a numerical implementation of the convergent variation, a previously proposed greedy technique is coupled with linear optimization. This algorithm allows a fully adaptive on-the-fly data dependent meshless selection of test and trial spaces. The new method satisfies the assumptions of the background theory, and numerical experiments demonstrate its stability.

引用

页码：1097 / 1115

页数：19

共 17 条

[1]

Atluri S.N., 2002, MESHLESS LOCAL PETRO

[2] ALGORITHMS FOR BEST L1 AND LINFINITY LINEAR APPROXIMATIONS ON A DISCRETE SET [J].

BARRODALE, I ;

YOUNG, A .

NUMERISCHE MATHEMATIK, 1966, 8 (03) :295-+

[3] Solving partial differential equations by collocation using radial basis functions [J].

Franke, C ;

Schaback, R .

APPLIED MATHEMATICS AND COMPUTATION, 1998, 93 (01) :73-82

[4] Convergence order estimates of meshless collocation methods using radial basis functions [J].

Franke, C ;

Schaback, R .

ADVANCES IN COMPUTATIONAL MATHEMATICS, 1998, 8 (04) :381-399

[5]

GLOBERG MA, 2000, ENG ANAL BOUNDARY EL, V24, P7

[6] On unsymmetric collocation by radial basis functions [J].

Hon, YC ;

Schaback, R .

APPLIED MATHEMATICS AND COMPUTATION, 2001, 119 (2-3) :177-186

[7] MULTIQUADRICS - A SCATTERED DATA APPROXIMATION SCHEME WITH APPLICATIONS TO COMPUTATIONAL FLUID-DYNAMICS .1. [J].

KANSA, EJ .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 1990, 19 (8-9) :127-145

[8] MULTIQUADRICS - A SCATTERED DATA APPROXIMATION SCHEME WITH APPLICATIONS TO COMPUTATIONAL FLUID-DYNAMICS .2. SOLUTIONS TO PARABOLIC, HYPERBOLIC AND ELLIPTIC PARTIAL-DIFFERENTIAL EQUATIONS [J].

KANSA, EJ .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 1990, 19 (8-9) :147-161

[9] Circumventing the ill-conditioning problem with multiquadric radial basis functions: Applications to elliptic partial differential equations [J].

Kansa, EJ ;

Hon, YC .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2000, 39 (7-8) :123-137

[10]

Ladyzhenskaya O. A., 1985, The Boundary Value Problems of Mathematical Physics

← 1 2 →