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An Extended Error Analysis for a Meshfree Discretization Method of Darcy's Problem

Schräder, Daniela and Wendland, Holger (2012) An Extended Error Analysis for a Meshfree Discretization Method of Darcy's Problem. Siam Journal on Numerical Analysis, 50 (2), pp. 838-857. Society for Industrial and Applied Mathematics. DOI: 10.1137/100806461. ISSN 0036-1429.

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Official URL: http://www.siam.org/journals/ojsa.php

Abstract

Recently [D. Schräder and H. Wendland, Math. Comp., 80 (2011), pp. 263–277], a new meshfree approximation method for Darcy’s problem has been introduced and analyzed. This method is based on a symmetric collocation approach using radial basis functions producing solutions with an analytically divergence-free velocity part. However, the error analysis provided in that paper works only for smooth solutions, where the smoothness is intrinsically linked to the smoothness of the employed basis function. In this paper, we will extend the error analysis to less smooth functions, showing that the approximation order for rougher solutions is determined by the smoothness of the solution rather than the smoothness of the basis function.

Document Type:Article
Title:An Extended Error Analysis for a Meshfree Discretization Method of Darcy's Problem
Authors:
AuthorsInstitution or Email of Authors
Schräder, Danieladaniela.schraeder@dlr.de
Wendland, HolgerUniversity of Oxford
Date:2012
Journal or Publication Title:Siam Journal on Numerical Analysis
Refereed publication:Yes
In SCOPUS:Yes
In ISI Web of Science:Yes
Volume:50
DOI:10.1137/100806461
Page Range:pp. 838-857
Publisher:Society for Industrial and Applied Mathematics
ISSN:0036-1429
Status:Published
Keywords:partial differential equations, radial basis functions, high-order method, collocation, error analysis
HGF - Research field:Aeronautics, Space and Transport
HGF - Program:Aeronautics
HGF - Program Themes:Aircraft Research (old)
DLR - Research area:Aeronautics
DLR - Program:L AR - Aircraft Research
DLR - Research theme (Project):L - Systems & Cabin (old)
Location: Göttingen
Institutes and Institutions:Institute of Aerodynamics and Flow Technology > Fluid Systems
Deposited By: Daniela Schräder
Deposited On:26 Sep 2012 14:30
Last Modified:24 Apr 2015 15:23

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