Analysis and convergence of a covolume method for the generalized stokes problem

Mathematics of Computation

Volumn 66, Issue 217, 1997, Pages 85-104

  Chou, S H ^a  

^a BOWLING GREEN STATE UNIVERSITY   (United States)

Author keywords

Augmented Lagrangian method; Covolume methods; Network models; Nonconforming mixed finite element

Indexed keywords

EID: 0031539622     PISSN: 00255718     EISSN: None     Source Type: Journal    
DOI: 10.1090/s0025-5718-97-00792-8     Document Type: Article

References (20)

1. R. Amit, C. A. Hall and T. A. Porsching, An application of network theory to the solution of implicit Navier-Stokes difference equations, J. Compt. Phys. 40 (1981), 183-201. MR 84d:76016
2. F. Brezzi and M. Fortin, Mixed and hybrid finite elements, Springer-Verlag, New York (1991). MR 92d:65187.
3. S. C. Brenner and L. Ridgway Scott, The mathematical theory of finite element methods, Springer-Verlag, 1994. MR 95f:65001
4. S. H. Chou, A network model for incompressible two-fluid flow and its numerical solution, Numer. Meth. Partial Diff. Eqns. 5 (1989), 1-21. MR 90i:76142
5. _,A network model for two-fluid flow, Proceedings of the 5th International Conference on Reactor Thermal Hydraulics, American Nuclear Society, Vol. VI, Salt Lake City, Utah, 1992, pp. 1607-1614.
6. S. Choudhury and R. A. Nicolaides, Discretization of incompressible vorticity-velocity equations on triangular meshes, Internat. J. Numer. Methods Fluid Dynamics 11 (1990).
7. M. Crouzeix and P. A. Raviart, Conforming and nonconforming finite element methods for solving the stationary stokes equations, RAIRO Anal. Numer. 7, (1973), 33-76. MR 49:8401
8. M, Fortin and R. Glowinski, Augmented Lagrangian methods: applications to the numerical solution of boundary-value problems, North-Holland, New York, 1983. MR 85a:49004
9. L. Gastaldi and R. Nochetto, Optimal L∞-error estimates for nonconforming and mixed finite element methods of lowest order, Numer. Math. 50 (1987), 587-61. MR 88f:65196
10. V. Girault and P. A. Raviart, Finite element methods for Navier-Stokes equations, Springer-Verlag, Berlin, and New York, 1986. MR 88b:65129
11. R. Glowinski and P. Le Tallec, Augmented Lagrangian and operator-splitting methods in nonlinear mechanics, SIAM, Philadelphia, PA, 1989. MR 91f:73038
12. C. A. Hall, J. C. Cavendish and W. H. Frey, The dual variable method for solving fluid flow difference equations on Delaunay triangulations, Comput. & Fluids 20 (1991), 145-164. MR 92g:76059
13. C. A. Hall, T. A. Porsching and G. L. Mesina, On a network method for unsteady incompressible fluid flow on triangular grids, Internat. J. Numer. Methods Fluids 15 (1992), 1383-4406.
14. F. H. Harlow and F. E. Welch, Numerical calculations of time dependent viscous incompressible flow of fluid with a free surface, Phys. Fluids 8 (1965), 2181.
15. R. A. Nicolaides, Direct discretization of planar div-curl problem, SIAM J. Numer. Anal. 29 (1992), 32-56. MR 93b:65176
16. R. A. Nicolaides, Analysis and convergence of the MAC scheme, SIAM J. Numer. Anal. 29 (1992), 1579-1591. MR 93j:65143
17. R. A. Nicolaides, T. A. Porsching and C. A. Hall, Covolume methods in computational fluid dynamics, Computational Fluid Dynamics Review (M. Hafez and K. Oshma, eds.), Wiley, New York, 1995, pp. 279-299.
18. T. A. Porsching, Error estimates for MAC-like approximations to the linear Navier-Stokes equations, Numer. Math. 29 (1978), 291-306. MR 57:11348
19. _,A network model for two-fluid flow, Numer. Methods Partial Differential Equations 1 (1985), 295-313.
20. G. Strang, Introduction to applied mathematics, Wellesley-Cambridge Press, Wellesley, MA, 1986. MR 88a:00006