Multigrid methods for saddle point problems: Stokes and Lamé systems

• Published in: Numerische Mathematik Vol. 128; no. 2; pp. 193 - 216
• Main Authors: Brenner, Susanne C., Li, Hengguang, Sung, Li-Yeng
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.10.2014
• Subjects: Mathematical and Computational Engineering; Mathematical and Computational Physics; Mathematical Methods in Physics; Mathematics; Mathematics and Statistics; Numerical Analysis; Numerical and Computational Physics; Simulation; Theoretical; Primary 65N55; 65F10; Secondary 76D07; 74B05; 65N30

We develop new multigrid methods for a class of saddle point problems that include the Stokes system in fluid flow and the Lamé system in linear elasticity as special cases. The new smoothers in the multigrid methods involve optimal preconditioners for the discrete Laplace operator. We prove uniform...