Recovery of functions from weak data using unsymmetric meshless kernel-based methods

被引：7
|
作者：
Schaback, Robert [1 ]
机构：
[1] Inst Numer & Angew Math, D-37083 Gottingen, Germany
来源：
APPLIED NUMERICAL MATHEMATICS | 2008年 / 58卷 / 05期
关键词：
approximation convolution; least squares; Petrov-Galerkin; overdetermined systems; error bounds; stability;
D O I：
10.1016/j.apnum.2007.02.009
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Recent engineering applications successfully introduced unsymmetric meshless local Petrov-Galerkin (MLPG) schemes. As a step towards their mathematical analysis, this paper investigates nonstationary unsymmetric Petrov-Galerkin-type meshless kernel-based methods for the recovery of L) functions from finitely many weak data. The results cover solvability conditions and error bounds in negative Sobolev norms with partially optimal rates. These rates are mainly determined by the approximation properties of the trial space, while choosing sufficiently many test functions ensures stability. Numerical examples are provided, supporting the theoretical results and leading to new questions for future research. (C) 2007 IMACS. Published by Elsevier B.V. All rights reserved.
引用
收藏
页码：726 / 741
页数：16
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