A finite element method for surface PDEs: matrix properties
A finite element method for surface PDEs: matrix properties
复制标题
DOI：
10.1007/s00211-009-0260-4
复制
发表时间：
2009-12
影响因子：
2.1
通讯作者：
M. Olshanskii;Arnold Reusken
中科院分区：
文献类型：
--
作者：
M. Olshanskii;Arnold Reusken
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 theH1and in theL2-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 likeh−3| lnh| andh−2| lnh|, respectively, wherehis the mesh size of the outer triangulation.
