Stable discretizations and IETI-DP solvers for the Stokes system in multi-patch Isogeometric Analysis
J Sogn, S Takacs - arXiv preprint arXiv:2202.13707, 2022 - arxiv.org
J Sogn, S Takacs
arXiv preprint arXiv:2202.13707, 2022•arxiv.orgWe are interested in a fast solver for the Stokes equations, discretized with multi-patch
Isogeometric Analysis. In the last years, several inf-sup stable discretizations for the Stokes
problem have been proposed, often the analysis was restricted to single-patch domains. We
focus on one of the simplest approaches, the isogeometric Taylor--Hood element. We show
how stability results for single-patch domains can be carried over to multi-patch domains.
While this is possible, the stability strongly depends on the shape of the geometry. We …
Isogeometric Analysis. In the last years, several inf-sup stable discretizations for the Stokes
problem have been proposed, often the analysis was restricted to single-patch domains. We
focus on one of the simplest approaches, the isogeometric Taylor--Hood element. We show
how stability results for single-patch domains can be carried over to multi-patch domains.
While this is possible, the stability strongly depends on the shape of the geometry. We …
We are interested in a fast solver for the Stokes equations, discretized with multi-patch Isogeometric Analysis. In the last years, several inf-sup stable discretizations for the Stokes problem have been proposed, often the analysis was restricted to single-patch domains. We focus on one of the simplest approaches, the isogeometric Taylor--Hood element. We show how stability results for single-patch domains can be carried over to multi-patch domains. While this is possible, the stability strongly depends on the shape of the geometry. We construct a Dual-Primal Isogeometric Tearing and Interconnecting (IETI-DP) solver that does not suffer from that effect. We give a convergence analysis and provide numerical tests.
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