A finite element method for surface PDEs: matrix properties View Full Text


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Article Info

DATE

2010-01

AUTHORS

Maxim A. Olshanskii, Arnold Reusken

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 H1 and in the L2-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. More... »

PAGES

491

References to SciGraph publications

  • 1988. Finite Elements for the Beltrami operator on arbitrary surfaces in PARTIAL DIFFERENTIAL EQUATIONS AND CALCULUS OF VARIATIONS
  • Journal

    TITLE

    Numerische Mathematik

    ISSUE

    3

    VOLUME

    114

    Author Affiliations

    Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/s00211-009-0260-4

    DOI

    http://dx.doi.org/10.1007/s00211-009-0260-4

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1006465796


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