Numerische Mathematik

, Volume 90, Issue 3, pp 441–458

Multigrid algorithms for a vertex–centered covolume method for elliptic problems

Authors

  • So-Hsiang Chou
    • Department of Mathematics and Statistics, Bowling Green State University, Bowling Green, OH 43403-0221, USA; e-mail: chou@zeus.bgsu.edu
  • Do Y. Kwak
    • Department of Mathematics, Korea Advanced Institute of Science and Technology, Taejon, Korea 305–701; e-mail: dykwak@math.kaist.ac.kr
Original article

DOI: 10.1007/s002110100288

Cite this article as:
Chou, S. & Kwak, D. Numer. Math. (2002) 90: 441. doi:10.1007/s002110100288

Summary.

We analyze V–cycle multigrid algorithms for a class of perturbed problems whose perturbation in the bilinear form preserves the convergence properties of the multigrid algorithm of the original problem. As an application, we study the convergence of multigrid algorithms for a covolume method or a vertex–centered finite volume element method for variable coefficient elliptic problems on polygonal domains. As in standard finite element methods, the V–cycle algorithm with one pre-smoothing converges with a rate independent of the number of levels. Various types of smoothers including point or line Jacobi, and Gauss-Seidel relaxation are considered.

Mathematics Subject Classification (1991): 65N15, 65N30

Copyright information

© Springer-Verlag Berlin Heidelberg 2002