A high-order, analytically divergence-free discretization method for Darcy’s problem
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- by Daniela Schräder and Holger Wendland PDF
- Math. Comp. 80 (2011), 263-277 Request permission
Abstract:
We develop and analyze a meshfree discretization method for Darcy’s problem. Our approximation scheme is based upon optimal recovery which leads to a collocation scheme using divergence-free positive definite kernels. Besides producing analytically incompressible flow fields, our method can be of arbitrary order, works in arbitrary space dimension and for arbitrary geometries. After deriving the scheme, we investigate the approximation error for smooth target functions and derive optimal approximation orders. Finally, we illustrate the method by giving numerical examples.References
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Additional Information
- Daniela Schräder
- Affiliation: Department of Mathematics, University of Sussex, Brighton, BN1 9RF, England
- Email: d.schraeder@sussex.ac.uk
- Holger Wendland
- Affiliation: Mathematical Institute, University of Oxford, 24-29 St Giles’, Oxford, OX1 3LB, England
- MR Author ID: 602098
- Email: holger.wendland@maths.ox.ac.uk
- Received by editor(s): December 2, 2008
- Received by editor(s) in revised form: November 2, 2009
- Published electronically: June 7, 2010
- © Copyright 2010 American Mathematical Society
- Journal: Math. Comp. 80 (2011), 263-277
- MSC (2010): Primary 65N15, 65N35
- DOI: https://doi.org/10.1090/S0025-5718-2010-02388-9
- MathSciNet review: 2728979