### Abstract

Language | English |
---|---|

Pages | 41-63 |

Number of pages | 23 |

Journal | ETNA - Electronic Transactions on Numerical Analysis |

Volume | 49 |

DOIs | |

Publication status | Published - 20 Apr 2018 |

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### Keywords

- Stokes problem
- nearly incompressible elasticity
- Taylor-Hood
- hybrid discontinuous Galerkin methods
- domain decomposition
- coarse space
- optimized restricted additive Schwarz methods

### Cite this

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**Numerical assessment of two-level domain decomposition preconditioners for incompressible Stokes and elasticity equations.** / Barrenechea, Gabriel R.; Bosy, Michał; Dolean, Victorita.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Numerical assessment of two-level domain decomposition preconditioners for incompressible Stokes and elasticity equations

AU - Barrenechea, Gabriel R.

AU - Bosy, Michał

AU - Dolean, Victorita

PY - 2018/4/20

Y1 - 2018/4/20

N2 - Solving the linear elasticity and Stokes equations by an optimal domain decomposition method derived algebraically involves the use of non standard interface conditions. The one-level domain decomposition preconditioners are based on the solution of local problems. This has the undesired consequence that the results are not scalable, it means that the number of iterations needed to reach convergence increases with the number of subdomains. This is the reason why in this work we introduce, and test numerically, two-level preconditioners. Such preconditioners use a coarse space in their construction. We consider the nearly incompressible elasticity problems and Stokes equations, and discretise them by using two finite element methods, namely, the hybrid discontinuous Galerkin and Taylor-Hood discretisations.

AB - Solving the linear elasticity and Stokes equations by an optimal domain decomposition method derived algebraically involves the use of non standard interface conditions. The one-level domain decomposition preconditioners are based on the solution of local problems. This has the undesired consequence that the results are not scalable, it means that the number of iterations needed to reach convergence increases with the number of subdomains. This is the reason why in this work we introduce, and test numerically, two-level preconditioners. Such preconditioners use a coarse space in their construction. We consider the nearly incompressible elasticity problems and Stokes equations, and discretise them by using two finite element methods, namely, the hybrid discontinuous Galerkin and Taylor-Hood discretisations.

KW - Stokes problem

KW - nearly incompressible elasticity

KW - Taylor-Hood

KW - hybrid discontinuous Galerkin methods

KW - domain decomposition

KW - coarse space

KW - optimized restricted additive Schwarz methods

U2 - 10.1553/etna_vol49s41

DO - 10.1553/etna_vol49s41

M3 - Article

VL - 49

SP - 41

EP - 63

JO - ETNA - Electronic Transactions on Numerical Analysis

T2 - ETNA - Electronic Transactions on Numerical Analysis

JF - ETNA - Electronic Transactions on Numerical Analysis

SN - 1068-9613

ER -