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Multigrid methods for Hdiv-conforming discontinuous Galerkin methods for the Stokes equations
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Published/Copyright:
August 7, 2015
Abstract
A multigrid method for the Stokes system discretized with an Hdiv-conforming discontinuous Galerkin method is presented. It acts on the combined velocity and pressure spaces and thus does not need a Schur complement approximation. The smoothers used are of overlapping Schwarz type and employ a local Helmholtz decomposition. Additionally, we use the fact that the discretization provides nested divergence free subspaces. We present the convergence analysis and numerical evidence that convergence rates are not only independent of mesh size, but also reasonably small.
Received: 2013-10-13
Accepted: 2014-1-14
Published Online: 2015-8-7
Published in Print: 2015-3-1
© 2015 by Walter de Gruyter Berlin/Boston
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Articles in the same Issue
- Frontmatter
- A multipoint Birkhoff type boundary value problem
- Performance estimation of linear algebra numerical libraries
- Finite element analysis of the stationary power-law Stokes equations driven by friction boundary conditions
- Chebyshev polynomials and best approximation of some classes of functions
- Multigrid methods for Hdiv-conforming discontinuous Galerkin methods for the Stokes equations
- Unified error bounds for all Newton–Cotes quadrature rules
- Optimal bilinear control of eddy current equations with grad–div regularization
Articles in the same Issue
- Frontmatter
- A multipoint Birkhoff type boundary value problem
- Performance estimation of linear algebra numerical libraries
- Finite element analysis of the stationary power-law Stokes equations driven by friction boundary conditions
- Chebyshev polynomials and best approximation of some classes of functions
- Multigrid methods for Hdiv-conforming discontinuous Galerkin methods for the Stokes equations
- Unified error bounds for all Newton–Cotes quadrature rules
- Optimal bilinear control of eddy current equations with grad–div regularization
