Analysis of a discontinuous finite element method for the coupled stokes and Darcy problems

Journal of Scientific Computing

Volumn 22-23, Issue , 2005, Pages 479-500

  Riviére, Béatrice ^a  

^a UNIVERSITY OF PITTSBURGH   (United States)

Author keywords

Error estimates; Interface conditions; Surface and subsurface flow

Indexed keywords

ERROR ANALYSIS; ESTIMATION; FINITE ELEMENT METHOD; FLUID DYNAMICS; MATHEMATICAL MODELS; PROBLEM SOLVING;

ERROR ESTIMATES; INTERFACE CONDITIONS; STOKES AND DARCY EQUATIONS; SURFACE AND SUBSURFACE FLOW;

GALERKIN METHODS;

EID: 17444430004     PISSN: 08857474     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10915-004-4147-3     Document Type: Article

References (22)

1. Adams, R. (1975). Sobolev Spaces, Academic Press, New York.
2. Arnold, D. N. (1982). An interior penalty finite element method with discontinuous elements. SIAM J. Numer. Anal. 19(4), 742-760.
3. Beavers, G. S., and Joseph, D. D. (1967). Boundary conditions at a naturally impermeable wall. J. Fluid. Mech. 30, 197-207.
4. Bernardi, C., Hecht, F., and Pironneau, O. (2002). Coupling Darcy and Stokes Equations for Porous Media with Cracks, Technical Report R02042, Paris VI.
5. 1 vector fields Mathematics of Computation, S 0025-5718(03)01579-5, Article electronically published.
6. Crouzeix, M., and Falk, R. S. (1989). Non conforming finite elements for the Stokes problem. Math. of Comp. 52, 437-456.
7. Crouzeix, M., and Raviart, P.-A. (1973). Conforming and nonconforming finite element methods for solving the stationary Stokes equations. I. Rev. Française Automat. Informat. Recherche Opérationnelle Sér. Rouge. 7(R-3), 33-75.
8. Discacciati, M., Miglio, E., and Quarteroni, A. (2001). Mathematical and numerical models for coupling surface and groundwater flows. Appl. Numer. Math. 43(1-2), 57-74, 2002. 19th Dundee Biennial Conference on Numerical Analysis.
9. Discacciati, M., and Quarteroni, A. (2003). Analysis of a domain decomposition method for the coupling of stokes and darcy equations. In Brezzi et al. (eds.) Numerical Analysis and Advanced Applications - Enumath 2001, Springer, Milan, pp. 3-20.
10. Ewing, R. E., Iliev, O. P., and Lazarov, R. D. (1992). Numerical Simulation of Contamination Transport Due to Flow in Liquid and Porous Media, Technical Report 1992-10, Enhanced Oil Recovery Institute, University of Wyoming.
11. Fortin, M., and Soulié, M. (1983). A non-conforming piecewise quadratic finite element on triangles. Int. J. Nume. Methods Eng., 19, 505-520.
12. Girault, V., Rivière, B., and Wheeler, M. F. (2002). A Discontinuous Galerkin Method With Non-Overlapping Domain Decomposition for the Stokes and Navier-Stokes Problems, Technical Report TICAM 02-08, to appear in Mathematics of Computation.
13. Girault, V., and Raviart, P.-A. (1986). Finite element methods for Navier-Stokes Equations, Springer-Verlag, Berlin.
14. Jäger, W., and Mikelić, A. (2000). On the interface boundary condition of Beavers, Joseph, and Saffman. SIAM J. Appl. Math. 60, 1111-1127.
15. Layton, W. J., Schieweck, F., and Yotov, I. (2003). Coupling fluid flow with porous media flow. SIAM J. Numer. Anal. 40(6), 2195-2218.
16. Mardal, K.,E., Tai, X.-C., and Winther, R. (2002). A robust finite element method for Darcy-Stokes flow. SIAM J. Numer. Anal. 40(5), 1605-1631 (electronic).
17. Payne, L. E., and Straughan, B. (1998). Analysis of the boundary condition at the interface between a viscous fluid and a porous medium and related modelling questions. J. Math. Pures Appl. 77, 317-354.
18. Rivière, B., Wheeler, M. F., and Girault, V. (1999). Improved energy estimates for interior penalty, constrained and discontinuous Galerkin methods for elliptic problems. Part I. Comput. Geosci. 3, 337-360.
19. Rivière, B., Wheeler, M. F., and Girault, V. (2001). A priori error estimates for finite element methods based on discontinuous approximation spaces for elliptic problems. SIAM J. Numer. Anal. 39, 902-931.
20. Rivière, B., and Yotov, I. (2003). Locally conservative coupling of Stokes and Darcy flow. SIAM J. Numer. Anal. accepted, 2004.
21. Saffman, P. (1971). On the boundary condition at the surface of a porous media. Stud. Appl. Math. 50, 292-315.
22. Wheeler, M. F. (1978). An elliptic collocation-finite element method with interior penalties. SIAM J. Numer. Anal. 15(1), 152-161.