The method of Glowinski and Pironneaufor the unsteady stokes problem

Computers and Mathematics with Applications

Volumn 48, Issue 7-8, 2004, Pages 1191-1211

  Waters, L K ^a   Fix, G J ^a   Cox, C L ^a  

^a CLEMSON UNIVERSITY   (United States)

Author keywords

Finite element method; Glowinski Pironneau method; Stokes problem

Indexed keywords

ALGORITHMS; BOUNDARY CONDITIONS; FINITE ELEMENT METHOD; INCOMPRESSIBLE FLOW; NAVIER STOKES EQUATIONS; POISSON EQUATION; UNSTEADY FLOW; VISCOELASTICITY; VISCOUS FLOW;

BOUNDARY FUNCTION; GLOWINSKI-PIRONNEAU METHOD; INSTEADY STOKES PROBLEM; KOVASZNAY PROBLEM;

PROBLEM SOLVING;

EID: 14644399864     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.camwa.2004.10.015     Document Type: Article

References (15)

1. V. Girault, and P.A. Raviart Finite Element Methods for Navier-Stokes Equations 1986 Springer-Verlag Berlin
2. M.D. Gunzburger Finite Element Methods for Viscous Incompressible Flows 1989 Academic Press Berlin
3. R. Glowinski, and O. Pironneau Finite element methods for Navier-Stokes equations Anna. Rev. Fluid Mech. 23 1992 167 201
4. P. Saramito A new 0-scheme algorithm and incompressible FEM for viscoelastic fluid flows Math. Mod. and Num. Anal. 28 1994 1 34
5. R. Glowinski Numerical Methods for Nonlinear Variational Problems 1984 Springer-Verlag Boston
6. A.E. Caola, Y.L. Joo, R.C. Armstrong, and R.A. Brown Highly parallel time integration of viscoelastic flows J. Non-Newt. Fluid Mech. 100 2001 191 216
7. M.O. Bristeau, O. Pironneau, R. Glowinski, J. Periaux, P. Perrier, and G. Poirier Application of optimal control and finite element methods to the calculation of transonic flows and incompressible viscous flows B. Hunt Numerical Methods in Applied Fluid Dynamics 1980 Academic Press New York 203 312
8. R. Glowinski, and O. Pironneau On numerical methods for the Stokes problem R. Glowinski E.Y. Rodin O.C. Zienkiewicz Energy Methods in Finite Element Analysis 1979 Wiley New York 243 264
9. R. Glowinski, and O. Pironneau On a mixed finite element approximation of the Stokes problem (I) Numer. Math 33 1979 397 424
10. F. Thomasset Implementation of Finite Element Methods for Navier-Stokes Equations 1981 Springer-Verlag New York
11. J.P. Aubin Behavior of the error of the approximate solutions of boundary value problems for linear elliptic operators by Galerkin's and finite differencemethods Ann. Scuola Sup. Pisa 21 1967 599 637
12. J. Nitsche Ein Kriterium fur die Quasi-Optimalität des Ritzchen Verfahrens Numerische Mathematik 11 1968 346 348
13. S.C. Brenner, and L.R. Scott The Mathematical Theory of Finite Element Methods 1994 Springer-Verlag New York
14. L. Kovasznay Laminar flow behind a two-dimensional grid Proc. Cambridge Phil. Soc. 44 1948 58 62
15. available at R.S. Tuminaro, M. Heroux, S.A. Hutchinson, and J.N. Shadid Official Aztec User's Guide: Version 2.1 December 1999