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.
Similar content being viewed by others
Author information
Authors and Affiliations
Additional information
Received August 19, 1999 / Revised version received July 10, 2000 / Published online June 7, 2001
Rights and permissions
About this article
Cite this article
Chou, SH., Kwak, D. Multigrid algorithms for a vertex–centered covolume method for elliptic problems. Numer. Math. 90, 441–458 (2002). https://doi.org/10.1007/s002110100288
Issue Date:
DOI: https://doi.org/10.1007/s002110100288