Hybrid discontinuous Galerkin discretisation and domain decomposition preconditioners for the Stokes problem

Gabriel R. Barrenechea, Michał Bosy, Victorita Dolean, Frédéric Nataf, Pierre Henri Tournier

Research output: Contribution to journalArticle

  • 1 Citations

Abstract

Solving the Stokes equation by an optimal domain decomposition method derived algebraically involves the use of nonstandard interface conditions whose discretisation is not trivial. For this reason the use of approximation methods such as hybrid discontinuous Galerkin appears as an appropriate strategy: on the one hand they provide the best compromise in terms of the number of degrees of freedom in between standard continuous and discontinuous Galerkin methods, and on the other hand the degrees of freedom used in the nonstandard interface conditions are naturally defined at the boundary between elements. In this paper, we introduce the coupling between a well chosen discretisation method (hybrid discontinuous Galerkin) and a novel and efficient domain decomposition method to solve the Stokes system. We present the detailed analysis of the hybrid discontinuous Galerkin method for the Stokes problem with nonstandard boundary conditions. The full stability and convergence analysis of the discretisation method is presented, and the results are corroborated by numerical experiments. In addition, the advantage of the new preconditioners over more classical choices is also supported by numerical experiments.

LanguageEnglish
Number of pages20
JournalComputational Methods in Applied Mathematics
Early online date22 Mar 2018
DOIs
Publication statusE-pub ahead of print - 22 Mar 2018

Fingerprint

Domain decomposition methods
Discontinuous Galerkin
Stokes Problem
Galerkin methods
Domain Decomposition
Preconditioner
Interface Conditions
Discretization Method
Discretization
Discontinuous Galerkin Method
Domain Decomposition Method
Decomposition
Degree of freedom
Optimal Domain
Numerical Experiment
Stokes System
Experiments
Stokes Equations
Boundary conditions
Stability and Convergence

Keywords

  • domain decomposition
  • hybrid discontinuous Galerkin methods
  • restricted additive Schwarz methods
  • Stokes problem

Cite this

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Hybrid discontinuous Galerkin discretisation and domain decomposition preconditioners for the Stokes problem. / Barrenechea, Gabriel R.; Bosy, Michał; Dolean, Victorita; Nataf, Frédéric; Tournier, Pierre Henri.

In: Computational Methods in Applied Mathematics, 22.03.2018.

Research output: Contribution to journalArticle

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AU - Bosy, Michał

AU - Dolean, Victorita

AU - Nataf, Frédéric

AU - Tournier, Pierre Henri

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N2 - Solving the Stokes equation by an optimal domain decomposition method derived algebraically involves the use of nonstandard interface conditions whose discretisation is not trivial. For this reason the use of approximation methods such as hybrid discontinuous Galerkin appears as an appropriate strategy: on the one hand they provide the best compromise in terms of the number of degrees of freedom in between standard continuous and discontinuous Galerkin methods, and on the other hand the degrees of freedom used in the nonstandard interface conditions are naturally defined at the boundary between elements. In this paper, we introduce the coupling between a well chosen discretisation method (hybrid discontinuous Galerkin) and a novel and efficient domain decomposition method to solve the Stokes system. We present the detailed analysis of the hybrid discontinuous Galerkin method for the Stokes problem with nonstandard boundary conditions. The full stability and convergence analysis of the discretisation method is presented, and the results are corroborated by numerical experiments. In addition, the advantage of the new preconditioners over more classical choices is also supported by numerical experiments.

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