Hybrid discontinuous Galerkin discretisation and domain decomposition preconditioners for the Stokes problem
arXiv:1610.09207 · doi:10.1515/cmam-2018-0005
Abstract
Solving the Stokes equation by an optimal domain decomposition method derived algebraically involves the use of non standard 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 non standard 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 non standard boundary conditions. This analysis is supported by numerical evidence. In addition, the advantage of the new preconditioners over more classical choices is also supported by numerical experiments.
References in corpus (2)
Cited by in corpus (6)
- HDGlab: An open-source implementation of the hybridisable discontinuous Galerkin method in MATLAB
- Discontinuous Galerkin approximations in computational mechanics: hybridization, exact geometry and degree adaptivity
- HMG -- Homogeneous multigrid for HDG
- Uniform block-diagonal preconditioners for divergence-conforming HDG Methods for the generalized Stokes equations and the linear elasticity equations
- Stabilised hybrid discontinuous Galerkin methods for the Stokes problem with non-standard boundary conditions
- Numerical assessment of two-level domain decomposition preconditioners for incompressible Stokes and elasticity equations