Stable discretizations and IETI-DP solvers for the Stokes system in multi-patch Isogeometric Analysis
Numerical Analysis
2022-09-20 v2 Numerical Analysis
Abstract
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.
Cite
@article{arxiv.2202.13707,
title = {Stable discretizations and IETI-DP solvers for the Stokes system in multi-patch Isogeometric Analysis},
author = {Jarle Sogn and Stefan Takacs},
journal= {arXiv preprint arXiv:2202.13707},
year = {2022}
}