A least-squares finite element method for the Navier-Stokes equations

Journal of Computational Physics

Volumn 213, Issue 1, 2006, Pages 174-183

  Bolton, P ^a   Thatcher, R W ^a  

^a UNIVERSITY OF MANCHESTER   (United Kingdom)

Author keywords

Conservation of mass; Finite elements; First order; Least squares; Navier Stokes equations; Stress and stream functions

Indexed keywords

FINITE ELEMENT METHOD; ITERATIVE METHODS; LEAST SQUARES APPROXIMATIONS; LINEAR ALGEBRA; VISCOUS FLOW;

A-PLANE; CONSERVATION OF MASS; FINITE ELEMENT; FIRST ORDER; FIRST ORDER SYSTEMS; LEAST SQUARE; LEAST SQUARES FINITE ELEMENT METHODS; NAVIER-STOKES EQUATION; STREAMFUNCTIONS; STRESS FUNCTIONS;

NAVIER STOKES EQUATIONS;

EID: 31744433693     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2005.08.015     Document Type: Article

References (23)

1. D.M. Bedivan Error estimates for least squares finite element methods Comput. Math. Appl. 43 2002 1003-1020
2. P. Bochev Analysis of least-squares finite element methods for the Navier-Stokes equations SIAM J. Numer. Anal. 34 1997 1817-1844
3. P. Bochev M.D. Gunzburger Accuracy of least-squares methods for the Navier-Stokes equations Comput. Fluids 22 1993 549-563
4. P. Bochev M.D. Gunzburger Finite element methods of least squares type SIAM Rev. 40 1998 789-837
5. P. Bolton, A least-squares finite element method for the Stokes and Navier-Stokes equations, Ph.D. Thesis, UMIST, 2002.
6. P. Bolton R.W. Thatcher Least-squares finite element solutions of the Stokes equations for incompressible flow J. Comput. Phys. 203 2005 287-304
7. 2 least-squares finite element method for the velocity-vorticity-pressure Stokes equations with velocity boundary conditions Appl. Math. Comput. 130 2002 121-144
8. J.M. Deang M.D. Gunzburger Issues related to least-squares finite element methods for the Stokes equations SIAM J. Sci. Comput. 20 1998 878-906
9. G.J. Fix M.D. Gunzburger R.A. Nicolaides On finite element methods of the least squares type Comput. Math. Appl. 5 1979 87-98
10. G.J. Fix M.D. Gunzburger R.A. Nicolaides On mixed finite element methods for first order elliptic systems Numer. Math. 37 1981 29-48
11. V. Girault P. Raviart Finite element methods for Navier-Stokes equations Springer Series in Computational Mathematics 1986 Springer Berlin
12. M.D. Gunzburger Finite Element Methods for Viscous Incompressible Flows: A Guide to Theory, Practice, and Algorithms 1989 Academic Press New York
13. M.D. Gunzburger A. Roy Nicolaides, Incompressible Computational Fluid Dynamics: Trends and Advances 1993 Cambridge University Press Cambridge
14. B.-N. Jiang A least-squares finite element method for incompressible Navier-Stokes equations Int. J. Numer. Methods Fluids 14 1992 843-859
15. B.-N. Jiang The least-squares finite element method, theory and applications in computational fluid dynamics and electromagnetics Scientific Computation Series 1998 Springer Berlin
16. B.-N. Jiang T.L. Lin L.A. Povinelli Large-scale computation of incompressible viscous flows by least-squares finite element method Comput. Methods Appl. Mech. Eng. 114 1994 213-231
17. B.-N. Jiang L.A. Povinelli Least-squares finite element method for fluid dynamics Comput. Methods Appl. Mech. Eng. 81 1990 13-37
18. J.N. Reddy An Introduction to Nonlinear Finite Element Analysis 2004 Oxford University Press Oxford
19. D.G. Shepherd Elements of Fluid Mechanics 1965 Harcourt Brace and World, Inc. New York
20. D.J. Silvester R.W. Thatcher The effect of stability of mixed finite element approximations on the accuracy and rate of convergence of solutions Int. J. Numer. Meth. Fluids 6 1986 841-853
21. R.W. Thatcher, A least squares method for Stokes flow based on stress and stream functions, Manchester Centre for Computational Mathematics Report 330, Manchester University/UMIST, 1998.
22. R.W. Thatcher A least squares method for biharmonic problems SIAM J. Numer. Anal. 38 2000 1523-1539
23. O.C. Zienkiewicz R.L. Taylor Finite element method fifth ed. Fluid Dynamics vol. 3 2000 Butterworth-Heinemann London