Radial basis function interpolation in Sobolev spaces and its applications

被引：0

作者：

Zhang, Manping ^{[1
]}

机构：

[1] Fudan Univ, Sch Math Sci, Shanghai 200433, Peoples R China

[2] Chinese Acad Sci, Inst Computat Math, Beijing 100080, Peoples R China

来源：

JOURNAL OF COMPUTATIONAL MATHEMATICS | 2007年 / 25卷 / 02期

关键词：

Sobolev space; radial basis function; global data density; meshless method;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we study the method of interpolation by radial basis functions and give some error estimates in Sobolev space H-k(Omega) (k >= 1). With a special kind of radial basis function, we construct a basis in H-k (Omega) and derive a meshless method for solving elliptic partial differential equations. We also propose a method for computing the global data density.

引用

页码：201 / 210

页数：10

共 12 条

[1]

Brenner SC., 1998, MATH THEORY FINITE E

[2]

Buhmann MD., 2003, C MO AP C M, DOI 10.1017/CBO9780511543241

[3] LATTICES ADMITTING UNIQUE LAGRANGE INTERPOLATIONS [J].

CHUNG, KC ;

YAO, TH .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 1977, 14 (04) :735-743

[4]

Gilbarg D., 2001, ELLIPTIC PARTIAL DIF, DOI DOI 10.1007/978-3-642-61798-0

[5]

Madych W.R., 1988, Approx. Theory Appl, V4, P77, DOI [10.1090/S0025-5718-1990-0993931-7, DOI 10.1090/S0025-5718-1990-0993931-7]

[6] INTERPOLATION OF SCATTERED DATA - DISTANCE MATRICES AND CONDITIONALLY POSITIVE DEFINITE FUNCTIONS [J].

MICCHELLI, CA .

CONSTRUCTIVE APPROXIMATION, 1986, 2 (01) :11-22

[7]

Schaback R., 2001, Multivariate Approximation and Applications, P1

[8]

SCOTT LR, 1990, MATH COMPUT, V54, P483, DOI 10.1090/S0025-5718-1990-1011446-7

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

Wendland, H .

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

[10]

WU XT, 2004, NATURAL SCI J FUDAN, V43, P292

← 1 2 →