Abstract
We consider multigrid methods for discontinuous Galerkin \(H({\text {div}},\Omega )\)-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.
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The research of Qingguo Hong and Johannes Kraus was supported by the Austrian Science Fund Grant P22989. The research of Jinchao Xu was supported in part by NSF Grant DMS-1217142 and DOE Grant DE-SC0006903. The research of Ludmil Zikatanov was supported in part by NSF DMS-1217142 and NSF DMS-1418843.
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Hong, Q., Kraus, J., Xu, J. et al. A robust multigrid method for discontinuous Galerkin discretizations of Stokes and linear elasticity equations. Numer. Math. 132, 23–49 (2016). https://doi.org/10.1007/s00211-015-0712-y
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DOI: https://doi.org/10.1007/s00211-015-0712-y