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

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

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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.

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


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


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