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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. SIAM - 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.
| Item URL in elib: | https://elib.dlr.de/65045/ | |||||||||
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| Document Type: | Article | |||||||||
| Title: | An Extended Error Analysis for a Meshfree Discretization Method of Darcy's Problem | |||||||||
| Authors: |
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| Date: | 2012 | |||||||||
| Journal or Publication Title: | Siam Journal on Numerical Analysis | |||||||||
| Refereed publication: | Yes | |||||||||
| Open Access: | No | |||||||||
| Gold Open Access: | No | |||||||||
| In SCOPUS: | Yes | |||||||||
| In ISI Web of Science: | Yes | |||||||||
| Volume: | 50 | |||||||||
| DOI: | 10.1137/100806461 | |||||||||
| Page Range: | pp. 838-857 | |||||||||
| Publisher: | SIAM - 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: | Schräder, Daniela | |||||||||
| Deposited On: | 26 Sep 2012 14:30 | |||||||||
| Last Modified: | 06 Sep 2019 15:17 |
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