Finite volume methods with local refinement for convection-diffusion problems
type: Item
instance of: scholarly article
title: Finite volume methods with local refinement for convection-diffusion problems
zbMATH Open document ID: 0807.65113
DOI: 10.1007/BF02262107
author: Panayot S. Vassilevski
author: Raytcho D. Lazarov
author: Ilya D. Mishev
published in: Computing
publication date: 1995-02-28T00:00:00Z
review text: This paper deals with the construction of conservative cell-centered approximations on locally refined grids for convection-diffusion second- order elliptic equations that have optimal order of convergence and satisfy the discrete maximum principle. In order to produce monotone schemes for convection-diffusion problems a variety of upwinding strategies have been used for a long time. In this paper, while keeping the required regularity of the solution to \(H^ s\) for \(3/2\leq s\leq 3\), the authors derive monotone approximations on grids with local patch refinement, estimate the error in the natural discrete \(H^ 1\)-norm and prove convergence rates of \(O(h^{1/2})\), or \(O(h^{3/2})\) depending upon the interpolation (piecewise constant or linear) used and also depending if the simple or modified upwinding strategies are used. Computer experiments for a variety of convection-diffusion problems, including convection dominated ones, in support of theoretical results and to assess the applicability of the derived schemes and error bounds are presented.
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 65N50
Mathematics Subject Classification ID: 65N15
Mathematics Subject Classification ID: 65N12
Mathematics Subject Classification ID: 35J25
zbMATH DE Number: 647753
zbMATH Keywords: finite volume methods
zbMATH Keywords: grid refinement
zbMATH Keywords: numerical examples
zbMATH Keywords: conservative cell-centered approximations
zbMATH Keywords: second-order elliptic equations
zbMATH Keywords: convergence
zbMATH Keywords: discrete maximum principle
zbMATH Keywords: monotone schemes
zbMATH Keywords: upwinding
zbMATH Keywords: convection-diffusion problems
zbMATH Keywords: error bounds
reviewed by: Pavol Chocholatý
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 647753