Discretization of elliptic differential equations on curvilinear bounded domains with sparse grids
type: Item
instance of: scholarly article
title: Discretization of elliptic differential equations on curvilinear bounded domains with sparse grids
zbMATH Open document ID: 0846.65060
DOI: 10.1007/BF02238512
author: T. Dornseifer
author: Christoph Pflaum
published in: Computing
publication date: 1996-09-04T00:00:00Z
review text: The authors consider the approximation of the weak solutions of some linear elliptic partial differential equation using finite elements on sparse grids. They construct some sparse grid finite element spaces, an interpolation theory on sparse grids and a discretization algorithm for sparse grids using grid generation by transformation. They take into acocunt curvilinear bounded domains. The numerical results for some examples show a very good convergence in the discrete \(L^2\) norm although the boundary of the domain has a ``bad'' shape (reentrant corners, for example).
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 35J25
Mathematics Subject Classification ID: 65N12
Mathematics Subject Classification ID: 65N50
zbMATH DE Number: 878403
zbMATH Keywords: reentrant corners
zbMATH Keywords: weak solutions
zbMATH Keywords: finite elements
zbMATH Keywords: sparse grid
zbMATH Keywords: algorithm
zbMATH Keywords: grid generation
zbMATH Keywords: curvilinear bounded domains
zbMATH Keywords: numerical results
zbMATH Keywords: convergence
reviewed by: Calin Ioan Gheorghiu
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 878403