Paper Info
Title
A finite element method for surface PDEs: matrix properties
Abstract
We consider a recently introduced new finite element approach for the discretization of elliptic partial differential equations on surfaces. The main idea of this method is to use finite element spaces that are induced by triangulations of an “outer” domain to discretize the partial differential equation on the surface. The method is particularly suitable for problems in which there is a coupling with a problem in an outer domain that contains the surface, for example, two-phase flow problems. It has been proved that the method has optimal order of convergence both in the H 1 and in the L 2-norm. In this paper, we address linear algebra aspects of this new finite element method. In particular the conditioning of the mass and stiffness matrix is investigated. For the two-dimensional case we present an analysis which proves that the (effective) spectral condition number of the diagonally scaled mass matrix and the diagonally scaled stiffness matrix behaves like h −3| ln h| and h −2| ln h|, respectively, where h is the mesh size of the outer triangulation.
Year
DOI
Venue
2010
10.1007/s00211-009-0260-4
Numerische Mathematik
Keywords
Field
DocType
surface pdes,surface,level set method,partial differential equation,new finite element approach,mass matrix,new finite element method,matrix property,interface,elliptic partial differential equation,ln h,stiffness matrix,two-phase flow,finite element,finite element space,outer domain,outer triangulation,two phase flow,condition number,finite element method,linear algebra,order of convergence
Matrix (mathematics),Mathematical analysis,Direct stiffness method,Extended finite element method,Finite element method,Stiffness matrix,Partial differential equation,Mathematics,hp-FEM,Mixed finite element method
Journal
Volume
Issue
ISSN
114
3
0945-3245
Citations 
PageRank 
References 
11
1.32
3
Authors
2
Name
Order
Citations
PageRank
Maxim A. Olshanskii132642.23
Arnold Reusken230544.91