On Richardson extrapolation for finite difference methods on regular grids
type: Item
instance of: scholarly article
title: On Richardson extrapolation for finite difference methods on regular grids
zbMATH Open document ID: 0661.65092
DOI: 10.1007/BF01396048
author: Reinhard Fößmeier
published in: Numerische Mathematik
publication date: 1989-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/133363
review text: Difference solutions of partial differential equations can in certain cases be expanded by even powers of a discretization parameter h. If we have n solutions corresponding to different mesh widths \(h_ 1,...,h_ n\) we can improve the accuracy by Richardson extrapolation and get a solution of order 2n, yet only on the intersection of all grids used, i.e. normally on the coarsest grid. To interpolate this high order solution with the same accuracy in points not belonging to all grids, we need 2n points in an interval of length \((2n-1)h_ 1.\) This drawback can be avoided by combining such an interpolation with the extrapolation by h. In this case the approximation depends only on grid points in an interval of length \(3/2h_ 1\). The length of this interval is independent of the desired order. By combining this approach with the method of Kreiss, boundary conditions on curved boundaries can be discretized with a high order even on coarse grids.
Mathematics Subject Classification ID: 65N06
Mathematics Subject Classification ID: 65D05
Mathematics Subject Classification ID: 65B05
Mathematics Subject Classification ID: 41A05
zbMATH DE Number: 4080814
zbMATH Keywords: two-dimensional interpolation
zbMATH Keywords: finite differences
zbMATH Keywords: curved boundaries
zbMATH Keywords: Kreiss method
zbMATH Keywords: Richardson extrapolation
MaRDI profile type: Publication
cites work: Q3340076
cites work: Q5655750
cites work: Q4749146
cites work: High Order Fast Laplace Solvers for the Dirichlet Problem on General Regions
OpenAlex ID: W2412112397
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description: scientific article; zbMATH DE number 4080814