Multigrid algorithms for C0 interior penalty methods
Document Type
Article
Publication Date
12-1-2006
Abstract
Multigrid algorithms for C interior penalty methods for fourth order elliptic boundary value problems on polygonal domains are studied in this paper. It is shown that V-cycle, F-cycle and W-cycle algorithms are contractions if the number of smoothing steps is sufficiently large. The contraction numbers of these algorithms are bounded by Cm , where m is the number of presmoothing (and postsmoothing) steps, α is the index of elliptic regularity, and the positive constant C is mesh-independent. These estimates are established for a smoothing scheme that uses a Poisson solve as a preconditioner, which can be easily implemented because the C finite element spaces are standard spaces for second order problems. Furthermore the variable V-cycle algorithm is also shown to be an optimal preconditioner. © 2006 Society for Industrial and Applied Mathematics. 0 -α 0
Publication Source (Journal or Book title)
SIAM Journal on Numerical Analysis
First Page
199
Last Page
223
Recommended Citation
Brenner, S., & Sung, L. (2006). Multigrid algorithms for C0 interior penalty methods. SIAM Journal on Numerical Analysis, 44 (1), 199-223. https://doi.org/10.1137/040611835