Fulltext

The Approximation and Computation of a Basis of the Trace Space H 1/2

Klouček, Petr ; Sorensen, Danny ; Wightman, Jennifer

In: Journal of Scientific Computing, 2007, vol. 32, no. 1, p. 73-108

Ajouter à la liste personnelle
    Titre
    • The Approximation and Computation of a Basis of the Trace Space H 1/2
    Auteur
    • Klouček, Petr. Texas Learning and Computational Center, University of Houston, 4800, 77204, Calhoun, TX, USA
    • Sorensen, Danny. Department of Computational and Applied Math, Rice University, 6100 Main Street, 77005, Houston, TX, USA
    • Wightman, Jennifer. Department of Math and Statistics, Coastal Carolina University, P.O. Box 261954, 29528, Conway, SC, USA
    Type de document
    • Postprint
    Langue
    • Anglais
    Publié dans
    • Journal of Scientific Computing, 2007, vol. 32, no. 1, p. 73-108. Kluwer Academic Publishers-Plenum Publishers; http://www.springer-ny.com
    Autre version électronique
    Identifiant OAI-PMH
    • oai:doc.rero.ch:316645
    Summary
    We present a method for construction of an approximate basis of the trace space H 1/2 based on a combination of the Steklov spectral method and a finite element approximation. Specifically, we approximate the Steklov eigenfunctions with respect to a particular finite element basis. Then solutions of elliptic boundary value problems with Dirichlet boundary conditions can be efficiently and accurately expanded in the discrete Steklov basis. We provide a reformulation of the discrete Steklov eigenproblem as a generalized eigenproblem that we solve by the implicitly restarted Arnoldi method of ARPACK. We include examples highlighting the computational properties of the proposed method for the solution of elliptic problems on bounded domains using both a conforming bilinear finite element and a non-conforming harmonic finite element. In addition, we document the efficiency of the proposed method by solving a Dirichlet problem for the Laplace equation on a densely perforated domain