A finite element method for surface PDEs: Matrix properties
type: Item
instance of: scholarly article
title: A finite element method for surface PDEs: Matrix properties
zbMATH Open document ID: 1204.65136
author: Maxim A. Olshanskii
author: Arnold Reusken
published in: Numerische Mathematik
publication date: 2010-02-24T00:00:00Z
review text: A new finite element approach is introduced for the discretization of elliptic partial differential equations (PDEs) on surfaces. The finite element spaces are induced by triangulations of an `outer' domain. Applications are given to two-phase flow problems. The paper analyzes the two-dimensional case and shows that the (effective) spectral condition number of the diagonally scaled mass matrix and the diagonally scaled stiffness matrix behaves like \(h^{-3}|\log h|\) and \(h^{-2}|\log h|,\) respectively, where \(h\) is the meshsize of the outer triangulation. Examples are given.
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 58J32
Mathematics Subject Classification ID: 65N15
Mathematics Subject Classification ID: 76D45
Mathematics Subject Classification ID: 76T99
Mathematics Subject Classification ID: 58J05
zbMATH DE Number: 5674536
zbMATH Keywords: finite elements
zbMATH Keywords: elliptic PDE on a surface
zbMATH Keywords: numerical examples
zbMATH Keywords: two-phase flow problems
zbMATH Keywords: spectral condition number
zbMATH Keywords: outer triangulation
reviewed by: Jean Mawhin
MaRDI profile type: Publication
full work available at URL: s00211-009-0260-4
OpenAlex ID: W2053364845
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DOI: 10.1007/S00211-009-0260-4
description: scientific article; zbMATH DE number 5674536