A stabilized mixed finite element method for Darcy flow based on a multiscale decomposition of the solution

Computer Methods in Applied Mechanics and Engineering

Volumn 195, Issue 33-36, 2006, Pages 4036-4049

  Nakshatrala, K B ^a   Turner, D Z ^a   Hjelmstad, K D ^a   Masud, A ^b  

^a University of Illinois at Urbana Champaign   (United States)

^b 1120 Science and Engineering Offices   (United States)

Author keywords

Darcy flow; Mixed methods; Multiscale formulation; Stabilized finite elements

Indexed keywords

COMPUTATIONAL GEOMETRY; COMPUTER SIMULATION; CONVERGENCE OF NUMERICAL METHODS;

CONVERGENCE RATES; DARCY FLOW; DISTORTED ELEMENT GEOMETRIES; MIXED FINITE ELEMENT; MULTISCALE FORMULATION; MULTISCLAE DECOMPOSITION; STABILIZED FINITE ELEMENTS;

FINITE ELEMENT METHOD;

COMPUTATIONAL GEOMETRY; COMPUTER SIMULATION; CONVERGENCE OF NUMERICAL METHODS; FINITE ELEMENT METHOD;

EID: 33646169428     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2005.07.009     Document Type: Article

References (21)

1. Ayub M., and Masud A. A new stabilized formulation for convective-diffusive heat transfer. Numer. Heat Transfer, Part B 44 (2003) 1-23
2. Babuška I. Error bounds for finite element methods. Numer. Math. 16 (1971) 322-333
3. Baiocchi C., Brezzi F., and Franca L. Virtual bubbles and Galerkin-least-squares type methods (Ga.L.S.). Comput. Methods Appl. Mech. Engrg. 105 (1993) 125-141
4. Brezzi F., and Fortin M. Mixed and hybrid finite element methods. Springer Series in Computational Mathematics volume 15 (1991), Springer-Verlag, New York
5. Brezzi F., and Russo A. Choosing bubbles for advection-diffusion problems. Math. Models Methods Appl. Sci. 4 (1994) 571-587
6. Doughlas Jr. J., and Wang J. An absolutely stabilized finite element method for the Stokes problem. Math. Comput. 52 (1989) 495-508
7. Franca L.P., and Russo A. Unlocking with residual-free bubbles. Comput. Methods Appl. Mech. Engrg. 142 (1997) 361-364
8. Hughes T.J.R. The Finite Element Method: Linear Static and Dynamic Finite Element Analysis (1987), Prentice-Hall, Englewood Cliffs, New Jersey
9. Hughes T.J.R. Multiscale phenomena: Green's functions, the Dirichlet-to-Neumann formulation, subgrid scale models, bubbles and the origins of stabilized methods. Comput. Methods Appl. Mech. Engrg. 127 (1995) 387-401
10. Hughes T.J.R., and Brooks A. Streamline-upwind/Petrov-Galerkin methods for convection dominated flows with emphasis on the incompressible Navier-Stokes equations. Comput. Methods Appl. Mech. Engrg. 32 (1982) 199-259
11. Hughes T.J.R., Franca L., and Hulbert G. A new finite element formulation for computational fluid dynamics: VIII. The Galerkin/least-squares method for advective-diffusive equations. Comput. Methods Appl. Mech. Engrg. 73 (1989) 173-189
12. T.J.R. Hughes, A. Masud, J. Wan, A stabilized mixed discontinuous Galerkin method for Darcy flow, Comput. Methods Appl. Mech. Engrg., in press, doi:10.1016/j.cma.2005.06.018.
13. Keener J.P. Principles of Applied Mathematics (2000), Perseus Books, Cambridge, Massachusetts
14. Masud A., and Bergman L.A. Application of multiscale finite element methods to the solution of the Fokker-Planck equation. Comput. Methods Appl. Mech. Engrg. 194 (2005) 1513-1526
15. Masud A., and Hughes T.J.R. A stabilized mixed finite element method for Darcy flow. Comput. Methods Appl. Mech. Engrg. 191 (2002) 4341-4370
16. Masud A., and Khurram R.A. A multiscale/stabilized finite element method for the advection-diffusion equation. Comput. Methods Appl. Mech. Engrg. 193 (2004) 1997-2018
17. A. Masud, R.A. Khurram, A multiscale finite element method for the incompressible Navier-Stokes equations, Comput. Methods Appl. Mech. Engrg., in press, doi:10.1016/j.cma.2005.05.048.
18. Naff R.F., Russell T.F., and Wilson J.D. Shape functions for three-dimensional control volume mixed finite element methods on irregular grids. In: Hassanizadeh S.M., et al. (Ed). Computational Methods in Water Resources vol. 1 (2002), Elsevier, Amsterdam 359-366
19. S.K. Singamsethi, Manufacture and performance of GFRP cuff joint for GFRP pultruded box sections, Master's thesis, University of Illinois at Urbana-Champaign, Urbana, USA, 2002.
20. Stakgold I. Green's Functions and Boundary Value Problems (1998), John Wiley & Sons, Inc., New York
21. D. Turner, A finite element approach to analyzing resin flow during injection for the GFRP cuff joint mold, Master's thesis, University of Illinois at Urbana-Champaign, Urbana, USA, 2003.