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

Schräder, Daniela and Wendland, Holger (2012) An Extended Error Analysis for a Meshfree Discretizatiion Method for Darcy's Problem. Siam Journal on Numerical Analysis, Vol. 50 (2), pp. 838-857. Society for Industrial and Applied Mathematics. DOI: 10.1137/100806461. ISSN 1095-7170.

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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 Discretizatiion Method for Darcy's Problem
Authors:
AuthorsInstitution or Email of Authors
Schräder, DanielaUNSPECIFIED
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:Vol. 50
DOI:10.1137/100806461
Page Range:pp. 838-857
Publisher:Society for Industrial and Applied Mathematics
ISSN:1095-7170
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
DLR - Research area:Aeronautics
DLR - Program:L AR - Aircraft Research
DLR - Research theme (Project):L - Systems & Cabin
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:04 Apr 2013 16:23

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