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A new approach for solving stokes systems arising from a distributive relaxation method
Author(s) -
Bacuta Constantin,
Vassilevski Panayot S.,
Zhang Shangyou
Publication year - 2011
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.20560
Subject(s) - mathematics , multigrid method , relaxation (psychology) , laplace operator , partial differential equation , block (permutation group theory) , laplace transform , diagonal , triangular matrix , stokes problem , discretization , distributive property , transformation (genetics) , block matrix , mathematical analysis , eigenvalues and eigenvectors , geometry , pure mathematics , finite element method , invertible matrix , psychology , social psychology , biochemistry , chemistry , physics , quantum mechanics , gene , thermodynamics
The distributed relaxation method for the Stokes problem has been advertised as an adequate change of variables that leads to a lower triangular system with Laplace operators on the main diagonal for which multigrid methods are very efficient. We show that under high regularity of the Laplacian, the transformed system admits almost block‐lower triangular form. We analyze the distributed relaxation method and compare it with other iterative methods for solving the Stokes system. We also present numerical experiments illustrating the effectiveness of the transformation which is well established for certain finite difference discretizations of Stokes problems. © 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 27: 898–914, 2011