Title: Multigrid algorithms for C0 interior penalty methods
Author: Susanne C. Brenner and Li-yeng Sung
Status: submitted
Abstract: Multigrid algorithms for C0 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^{-\alpha},
where m is the number of pre-smoothing (and post-smoothing)
steps, $\alpha$ 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
C0 finite element spaces are standard spaces for second order
problems. Furthermore the variable V-cycle algorithm is also
shown to be an optimal preconditioner.
Presented at:
- Schnelle Löser für partielle Differentialgleichungen,
June 1-6, 2003
- Recent Advances and State-of-the-Art in Discontinuous Galerkin
Methods in Computational Structural Mechanics, Army High Performance
Computing Research Center, Minneapolis, October 28-29, 2003
- Computational Methods in Multiscale Analysis and Applications,
University of Florida, Gainesville, February 29-March 2, 2004
- Modern Computational Methods in Applied Mathematics (MCM 2004),
B\c edlewo, Pozna\'n, Poland, June 14-19, 2004
- Mini-Symposium: Nonconforming Methods: Classical, Mortar and
Discontinuous Galerkin, ECCOMAS 2004, Jyv\"askyl\"a, Finland,
July 18-22, 2004
- International Conference of Numerical Analysis and Applied Mathematics
2004 (ICNAAM 2004), Chalkis, Greece, September 10-14, 2004
- Institute of Computational Mathematics, Chinese Academy of Science,
Beijing, PRC, September 7, 2004
paper