A robust multigrid method for discontinuous Galerkin discretizations of Stokes and linear elasticity equations. (English) Zbl 1338.76054
Summary: We consider multigrid methods for discontinuous Galerkin \(H(\operatorname{div},\Omega)\)-conforming discretizations of the Stokes and linear elasticity equations. We analyze variable V-cycle and W-cycle multigrid methods with nonnested bilinear forms. We prove that these algorithms are optimal and robust, i.e., their convergence rates are independent of the mesh size and also of the material parameters such as the Poisson ratio. Numerical experiments are conducted that further confirm the theoretical results.
MSC:
| 76M10 | Finite element methods applied to problems in fluid mechanics |
| 74S05 | Finite element methods applied to problems in solid mechanics |
| 65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |
| 65N55 | Multigrid methods; domain decomposition for boundary value problems involving PDEs |
| 74B05 | Classical linear elasticity |
| 76D07 | Stokes and related (Oseen, etc.) flows |
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