Multigrid analysis for the time dependent Stokes problem

Olshanskii, Maxim

doi:10.1090/S0025-5718-2011-02494-4

Multigrid analysis for the time dependent Stokes problem
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by Maxim A. Olshanskii PDF

Math. Comp. 81 (2012), 57-79 Request permission

Abstract:

Certain implicit time stepping procedures for the incompressible Stokes or Navier-Stokes equations lead to a singular-perturbed Stokes type problem at each time step. The paper presents a convergence analysis of a geometric multigrid solver for the system of linear algebraic equations resulting from the disretization of the problem using a finite element method. Several smoothing iterative methods are considered: a smoother based on distributive iterations, the Braess-Sarazin and inexact Uzawa smoother. Convergence analysis is based on smoothing and approximation properties in special norms. A robust (independent of time step and mesh parameter) estimate is proved for the two-grid and multigrid W-cycle convergence factors.

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