Multigrid methods for saddle point problems: Stokes and Lamé systems

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• 作者：Susanne C. Brenner ; Hengguang Li ; Li-Yeng Sung
• 关键词：Primary 65N55 ; 65F10 ; 65N30 ; Secondary 76D07 ; 74B05
• 刊名：Numerische Mathematik
• 出版年：2014
• 出版时间：October 2014
• 年：2014
• 卷：128
• 期：2
• 页码：193-216
• 全文大小：340 KB
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• 作者单位：Susanne C. Brenner (1)
  Hengguang Li (2)
  Li-Yeng Sung (1)
  
  1. Department of Mathematics and Center for Computation and Technology, Louisiana State University, Baton Rouge, LA, 70803, USA
  2. Department of Mathematics, Wayne State University, Detroit, MI?, 48202, USA
  
• ISSN：0945-3245

文摘

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 convergence of the \(W\) -cycle algorithm in the energy norm and present numerical results for \(W\) -cycle and \(V\) -cycle algorithms.