BDDC algorithms for incompressible Stokes equations

Jing Li, Olof Widlund

Research output: Contribution to journalArticle

Abstract

The purpose of this paper is to extend the balancing domain decomposition by constraints (BDDC) algorithm to saddle-point problems that arise when mixed finite element methods are used to approximate the system of incompressible Stokes equations. The BDDC algorithms are iterative substructuring methods which form a class of domain decomposition methods based on the decomposition of the domain of the differential equations into nonoverlapping subdomains. They are defined in terms of a set of primal continuity constraints which are enforced across the interface between the subdomains and which provide a coarse space component of the preconditioner. Sets of such constraints are identified for which bounds on the rate of convergence can be established that are just as strong as previously known bounds for the elliptic case. In fact, the preconditioned operator is effectively positive definite, which makes the use of a conjugate gradient method possible. A close connection is also established between the BDDC and dual-primal finite element tearing and interconnecting (FETI-DP) algorithms for the Stokes case.

Original languageEnglish (US)
Pages (from-to)2432-2455
Number of pages24
JournalSIAM Journal on Numerical Analysis
Volume44
Issue number6
DOIs
StatePublished - Dec 1 2006

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Keywords

  • Domain decomposition
  • Incompressible Stokes
  • Mixed finite elements
  • Preconditioners

ASJC Scopus subject areas

  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics

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