### Abstract

The purpose of this paper is to extend the BDDC (balancing domain decomposition by constraints) 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 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. The preconditioned operator is positive definite and a conjugate gradient method can be used. A close connection is also established between the BDDC and FETI-DP algorithms for the Stokes case.

Original language | English (US) |
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Title of host publication | Domain Decomposition Methods in Science and Engineering XVI |

Editors | Olof Widlund, David Keyes |

Pages | 413-420 |

Number of pages | 8 |

State | Published - 2007 |

### Publication series

Name | Lecture Notes in Computational Science and Engineering |
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Volume | 55 |

ISSN (Print) | 1439-7358 |

### ASJC Scopus subject areas

- Modeling and Simulation
- Engineering(all)
- Discrete Mathematics and Combinatorics
- Control and Optimization
- Computational Mathematics

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## Cite this

*Domain Decomposition Methods in Science and Engineering XVI*(pp. 413-420). (Lecture Notes in Computational Science and Engineering; Vol. 55).