Stable discretizations and IETI-DP solvers for the Stokes system in multi-patch Isogeometric Analysis

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 simp...

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Bibliographic Details
Main Authors Sogn, Jarle, Takacs, Stefan
Format Journal Article
LanguageEnglish
Published 28.02.2022
Subjects
Computer Science - Numerical Analysis
Mathematics - Numerical Analysis
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Summary: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.
DOI:10.48550/arxiv.2202.13707