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 - 2006

Fingerprint

Stokes Equations
Domain Decomposition
Balancing
Decomposition
Domain decomposition methods
Iterative Substructuring
Conjugate gradient method
FETI-DP
Iterative methods
Saddle Point Problems
Mixed Finite Element Method
Primal-dual
Domain Decomposition Method
Conjugate Gradient Method
Differential equations
Stokes
Preconditioner
Positive definite
Finite element method
Rate of Convergence

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics
  • Computational Mathematics

Cite this

BDDC algorithms for incompressible Stokes equations. / Li, Jing; Widlund, Olof.

In: SIAM Journal on Numerical Analysis, Vol. 44, No. 6, 2006, p. 2432-2455.

Research output: Contribution to journalArticle

Li, Jing ; Widlund, Olof. / BDDC algorithms for incompressible Stokes equations. In: SIAM Journal on Numerical Analysis. 2006 ; Vol. 44, No. 6. pp. 2432-2455.
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