Numerical construction of optimal adaptive grids in two spatial dimensions
type: Item
instance of: scholarly article
title: Numerical construction of optimal adaptive grids in two spatial dimensions
zbMATH Open document ID: 0964.65124
DOI: 10.1016/S0898-1221(00)00133-4
author: Tsu-Fen Chen
author: Haw-Dai Yang
publication date: 2001-06-26T00:00:00Z
review text: Disregarding work on optimal grids for the numerical solution of boundary value problems done by Bakhvalov, and also disregarding a large number of more recent papers on grids for two-dimensional convection-diffusion problems, see e.g. papers by Shishkin, Roos, Stynes, the authors consider a practical algorithm to obtain triangular grids for usual finite elements in the case of convection dominated problems. For this they start from a coarse uniform grid, compute the finite element solution and from here a partition of points along a special flow line, and then construct further points on level curves orthogonal to the flow line. Then follows a Delaunay triangulation of the obtained grid points. Many figures are shown with grids resulting for three academic examples (with constant velocity vector in the convection-diffusion equation). Here, it is visible that very long thin triangles may result, but the algorithm seems capable to catch a curved inner layer. Optimality of the grids is claimed since the \(H^1\)-norm of the error drops linearly with \(n^{-1/2}\), where \(n\) is the number of triangles.
reviewed by: Gisbert Stoyan
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 65N50
Mathematics Subject Classification ID: 35J25
zbMATH DE Number: 1471214
zbMATH Keywords: convection-diffusion problems
zbMATH Keywords: convection dominated problems
zbMATH Keywords: optimal adaptive grids
zbMATH Keywords: finite elements
zbMATH Keywords: Delaunay triangulation
zbMATH Keywords: algorithm
MaRDI profile type: Publication
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published in: Computers & Mathematics with Applications
description: scientific article; zbMATH DE number 1471214