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Media type:
E-Article
Title:
MULTIGRID ANALYSIS FOR THE TIME DEPENDENT STOKES PROBLEM
Contributor:
OLSHANSKII, MAXIM A.
Published:
American Mathematical Society, 2012
Published in:
Mathematics of Computation, 81 (2012) 277, Seite 57-79
Language:
English
DOI:
10.1090/S0025-5718-2011-02494-4
ISSN:
0025-5718;
1088-6842
Origination:
Footnote:
Description:
<p>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.</p>