Robust multigrid methods for isogeometric discretizations of the Stokes equations

@article{Takacs2017RobustMM,
  title={Robust multigrid methods for isogeometric discretizations of the Stokes equations},
  author={Stefan Takacs},
  journal={arXiv: Numerical Analysis},
  year={2017}
}
  • S. Takacs
  • Published 6 February 2017
  • Computer Science, Mathematics
  • arXiv: Numerical Analysis
In recent publications, the author and his coworkers have proposed a multigrid method for solving linear systems arizing from the discretization of partial differential equations in isogeometric analysis and have proven that the convergence rates are robust in both the grid size and the polynomial degree. So, far the method has only been discussed for the Poisson problem. In the present paper, we want to face the question if it is possible to extend the method to the Stokes equations. 
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SHOWING 1-10 OF 21 REFERENCES
IsoGeometric Analysis: Stable elements for the 2D Stokes equation
In this paper, we discuss the application of IsoGeometric Analysis to incompressible viscous flow problems. We consider, as a prototype problem, the Stokes system and we propose various choices of
Isogeometric discretizations of the Stokes problem: stability analysis by the macroelement technique
TLDR
This work proposes and study high-regularity isogeometric discretizations of the Stokes problem and addresses the Taylor‐Hoodisogeometric element and a newSubgridelement which allows highest regularity velocity and pressure fields.
A comparative study of efficient iterative solvers for generalized Stokes equations
TLDR
The main topic of the paper is a study of efficient iterative solvers for the resulting discrete saddle point problem, investigating a coupled multigrid method with Braess–Sarazin and Vanka‐type smoothers, a preconditioned MINRES method and an inexact Uzawa method.
Robust Multigrid for Isogeometric Analysis Based on Stable Splittings of Spline Spaces
TLDR
It is proved that the resulting multigrid method exhibits iteration numbers which are robust with respect to the spline degree and the mesh size, and can be efficiently realized for discretizations of problems in arbitrarily high geometric dimensio...
Isogeometric Analysis: new stable elements for the Stokes equation
SUMMARYIn this paper we discuss the application of IsoGeometric Analysis to incompressible viscous flow problems, forwhich preliminary results were presented in [1, 2, 3]. Here we consider, as a
ISOGEOMETRIC DIVERGENCE-CONFORMING B-SPLINES FOR THE STEADY NAVIER–STOKES EQUATIONS
TLDR
A comprehensive suite of numerical experiments are presented which indicate optimal convergence rates for both the discrete velocity and pressure fields for general configurations, suggesting that the a priori estimates may be conservative.
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