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Volumn 195, Issue 25-28, 2006, Pages 3347-3381

A stabilized mixed discontinuous Galerkin method for Darcy flow

Author keywords

Darcy flow; Discontinuous Galerkin method; Error estimates; Finite elements; Mass balance; Mixed method; Patch test; Stabilized method

Indexed keywords

COMPUTATIONAL GEOMETRY; ERROR ANALYSIS; ESTIMATION; FINITE ELEMENT METHOD; INTERPOLATION;

EID: 33645911505     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2005.06.018     Document Type: Article
Times cited : (84)

References (41)
  • 2
    • 0001163226 scopus 로고
    • An interior penalty finite element method with discontinuous element
    • Arnold D.N. An interior penalty finite element method with discontinuous element. SIAM J. Numer. Anal. 19 (1982) 742-760
    • (1982) SIAM J. Numer. Anal. , vol.19 , pp. 742-760
    • Arnold, D.N.1
  • 3
    • 0036410391 scopus 로고    scopus 로고
    • Unified analysis of discontinuous Galerkin methods for elliptic problems
    • Arnold D.N., Brezzi F., Cockburn B., and Marini L.D. Unified analysis of discontinuous Galerkin methods for elliptic problems. SIAM J. Numer. Anal. 39 (2002) 1749-1779
    • (2002) SIAM J. Numer. Anal. , vol.39 , pp. 1749-1779
    • Arnold, D.N.1    Brezzi, F.2    Cockburn, B.3    Marini, L.D.4
  • 4
    • 0242415937 scopus 로고    scopus 로고
    • A new stabilized formulation for convective-diffusive heat transfer
    • Ayub M., and Masud A. A new stabilized formulation for convective-diffusive heat transfer. Numer. Heat Transfer, Part B 44 (2003) 1-23
    • (2003) Numer. Heat Transfer, Part B , vol.44 , pp. 1-23
    • Ayub, M.1    Masud, A.2
  • 5
    • 0011029223 scopus 로고
    • Discontinuous finite element high order accurate numerical solution of the compressible Navier-Stokes equations
    • Morton K.W., et al. (Ed), Clarendon Press, Oxford
    • Bassi F., and Rebay S. Discontinuous finite element high order accurate numerical solution of the compressible Navier-Stokes equations. In: Morton K.W., et al. (Ed). Proceedings of the Conference "Numerical Methods for Fluid Dynamics V" (1995), Clarendon Press, Oxford 295-302
    • (1995) Proceedings of the Conference "Numerical Methods for Fluid Dynamics V" , pp. 295-302
    • Bassi, F.1    Rebay, S.2
  • 6
    • 0042824223 scopus 로고    scopus 로고
    • Superconvergence and H(div) projection for discontinuous Galerkin methods
    • Bastian P., and Riviére B. Superconvergence and H(div) projection for discontinuous Galerkin methods. Int. J. Numer. Methods Fluids 42 (2003) 1043-1057
    • (2003) Int. J. Numer. Methods Fluids , vol.42 , pp. 1043-1057
    • Bastian, P.1    Riviére, B.2
  • 7
    • 0345062335 scopus 로고    scopus 로고
    • A discontinuous hp finite element method for convection-diffusion problems
    • Baumann C.E., and Oden J.T. A discontinuous hp finite element method for convection-diffusion problems. Comput. Methods Appl. Mech. Engrg. 175 (1999) 311-341
    • (1999) Comput. Methods Appl. Mech. Engrg. , vol.175 , pp. 311-341
    • Baumann, C.E.1    Oden, J.T.2
  • 8
    • 0037474430 scopus 로고    scopus 로고
    • Energy norm a posteriori error estimation for discontinuous Galerkin methods
    • Becker R., Hansbo P., and Larson M.G. Energy norm a posteriori error estimation for discontinuous Galerkin methods. Comput. Methods Appl. Mech. Engrg. 192 (2003) 723-733
    • (2003) Comput. Methods Appl. Mech. Engrg. , vol.192 , pp. 723-733
    • Becker, R.1    Hansbo, P.2    Larson, M.G.3
  • 9
    • 2042520906 scopus 로고    scopus 로고
    • Improving stability and accuracy of plate finite elements via algebraic subgrid scale stabilization
    • Bischoff M., and Bletzinger K.U. Improving stability and accuracy of plate finite elements via algebraic subgrid scale stabilization. Comput. Methods Appl. Mech. Engrg. 193 15-16 (2004) 1517-1528
    • (2004) Comput. Methods Appl. Mech. Engrg. , vol.193 , Issue.15-16 , pp. 1517-1528
    • Bischoff, M.1    Bletzinger, K.U.2
  • 10
    • 2042488782 scopus 로고    scopus 로고
    • On inf-sup stabilized finite element methods for transient problems
    • Bochev P., Gunzburger M., and Shadid J. On inf-sup stabilized finite element methods for transient problems. Comput. Methods Appl. Mech. Engrg. 193 15-16 (2004) 1471-1489
    • (2004) Comput. Methods Appl. Mech. Engrg. , vol.193 , Issue.15-16 , pp. 1471-1489
    • Bochev, P.1    Gunzburger, M.2    Shadid, J.3
  • 13
    • 2042428741 scopus 로고    scopus 로고
    • Edge stabilization for Galerkin approximations of convection-diffusion problems
    • Burman E., and Hansbo P. Edge stabilization for Galerkin approximations of convection-diffusion problems. Comput. Methods Appl. Mech. Engrg. 193 15-16 (2004) 1437-1453
    • (2004) Comput. Methods Appl. Mech. Engrg. , vol.193 , Issue.15-16 , pp. 1437-1453
    • Burman, E.1    Hansbo, P.2
  • 14
    • 0041624307 scopus 로고    scopus 로고
    • A new stabilized finite element formulation for scalar convection-diffusion problems: the streamline and approximate upwind/Petrov-Galerkin method
    • Carmo E.G.D., and Alvarez G.B. A new stabilized finite element formulation for scalar convection-diffusion problems: the streamline and approximate upwind/Petrov-Galerkin method. Comput. Methods Appl. Mech. Engrg. 192 (2003) 3379-3396
    • (2003) Comput. Methods Appl. Mech. Engrg. , vol.192 , pp. 3379-3396
    • Carmo, E.G.D.1    Alvarez, G.B.2
  • 15
    • 0141569419 scopus 로고    scopus 로고
    • A superconvergence result for discontinuous Galerkin methods applied to elliptic problems
    • Castillo P. A superconvergence result for discontinuous Galerkin methods applied to elliptic problems. Comput. Methods Appl. Mech. Engrg. 192 (2003) 4675-4685
    • (2003) Comput. Methods Appl. Mech. Engrg. , vol.192 , pp. 4675-4685
    • Castillo, P.1
  • 16
    • 0036931450 scopus 로고    scopus 로고
    • Approximation of the velocity by coupling discontinuous Galerkin and mixed finite element methods for flow problems
    • Cockburn B., and Dawson C. Approximation of the velocity by coupling discontinuous Galerkin and mixed finite element methods for flow problems. Comput. Geosci. 6 (2002) 505-522
    • (2002) Comput. Geosci. , vol.6 , pp. 505-522
    • Cockburn, B.1    Dawson, C.2
  • 17
    • 2042453321 scopus 로고    scopus 로고
    • Approximation of the incompressible Navier-Stokes equations using orthogonal-subscale stabilization and pressure segregation on anisotropic finite element meshes
    • Codina R., and Soto O. Approximation of the incompressible Navier-Stokes equations using orthogonal-subscale stabilization and pressure segregation on anisotropic finite element meshes. Comput. Methods Appl. Mech. Engrg. 193 15-16 (2004) 1403-1419
    • (2004) Comput. Methods Appl. Mech. Engrg. , vol.193 , Issue.15-16 , pp. 1403-1419
    • Codina, R.1    Soto, O.2
  • 19
    • 0347930482 scopus 로고    scopus 로고
    • Coupled discontinuous and continuous Galerkin finite element methods for the depth-integrated shallow water equations
    • Dawson C., and Proft J. Coupled discontinuous and continuous Galerkin finite element methods for the depth-integrated shallow water equations. Comput. Methods Appl. Mech. Engrg. 193 (2004) 289-318
    • (2004) Comput. Methods Appl. Mech. Engrg. , vol.193 , pp. 289-318
    • Dawson, C.1    Proft, J.2
  • 20
    • 0242457671 scopus 로고    scopus 로고
    • Discontinuous/continuous Galerkin methods for coupling the primitive and wave continuity equations of shallow water
    • Dawson C., and Proft J. Discontinuous/continuous Galerkin methods for coupling the primitive and wave continuity equations of shallow water. Comput. Methods Appl. Mech. Engrg. 192 (2003) 5123-5145
    • (2003) Comput. Methods Appl. Mech. Engrg. , vol.192 , pp. 5123-5145
    • Dawson, C.1    Proft, J.2
  • 21
    • 0037436501 scopus 로고    scopus 로고
    • A discontinuous Galerkin method with Lagrange multipliers for the solution of Helmholtz problems in the mid-frequency regime
    • Farhat C., Harari I., and Hetmaniuk U. A discontinuous Galerkin method with Lagrange multipliers for the solution of Helmholtz problems in the mid-frequency regime. Comput. Methods Appl. Mech. Engrg. 192 (2003) 1389-1419
    • (2003) Comput. Methods Appl. Mech. Engrg. , vol.192 , pp. 1389-1419
    • Farhat, C.1    Harari, I.2    Hetmaniuk, U.3
  • 22
    • 0038702482 scopus 로고    scopus 로고
    • Pressure bubbles stabilization features in the Stokes problem
    • Franca L.P., and Oliveira S.P. Pressure bubbles stabilization features in the Stokes problem. Comput. Methods Appl. Mech. Engrg. 192 (2003) 1929-1937
    • (2003) Comput. Methods Appl. Mech. Engrg. , vol.192 , pp. 1929-1937
    • Franca, L.P.1    Oliveira, S.P.2
  • 23
    • 33645926273 scopus 로고    scopus 로고
    • L.P. Franca, A. Russo, A formulation based on residual-free bubbles for a singular perturbation equation, preprint.
  • 24
    • 2042524350 scopus 로고    scopus 로고
    • A three-level finite element method for the instationary incompressible Navier-Stokes equations
    • Gravemeier V., Wall W.A., and Ramm E. A three-level finite element method for the instationary incompressible Navier-Stokes equations. Comput. Methods Appl. Mech. Engrg. 193 15-16 (2004) 1323-1366
    • (2004) Comput. Methods Appl. Mech. Engrg. , vol.193 , Issue.15-16 , pp. 1323-1366
    • Gravemeier, V.1    Wall, W.A.2    Ramm, E.3
  • 25
    • 2042455855 scopus 로고    scopus 로고
    • Stability of semidiscrete formulations for parabolic problems at small time steps
    • Harari I. Stability of semidiscrete formulations for parabolic problems at small time steps. Comput. Methods Appl. Mech. Engrg. 193 15-16 (2004) 1491-1516
    • (2004) Comput. Methods Appl. Mech. Engrg. , vol.193 , Issue.15-16 , pp. 1491-1516
    • Harari, I.1
  • 26
    • 2042418174 scopus 로고    scopus 로고
    • Computing reactive flows with a field Monte Carlo formulation and multiscale methods
    • Hauke G., and Valino L. Computing reactive flows with a field Monte Carlo formulation and multiscale methods. Comput. Methods Appl. Mech. Engrg. 193 15-16 (2004) 1455-1470
    • (2004) Comput. Methods Appl. Mech. Engrg. , vol.193 , Issue.15-16 , pp. 1455-1470
    • Hauke, G.1    Valino, L.2
  • 27
    • 0029405472 scopus 로고
    • Multiscale phenomena: Green's functions, the Dirichlet-to-Neumann formulation, subgrid scale models, bubbles and the origins of stabilized methods
    • 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
    • (1995) Comput. Methods Appl. Mech. Engrg. , vol.127 , pp. 387-401
    • Hughes, T.J.R.1
  • 29
    • 0023450642 scopus 로고
    • A new finite element formulation for computational fluid dynamics: VII. The Stokes problem with various well posed boundary conditions: Symmetric formulations that converge for all velocity/pressure spaces
    • Hughes T.J.R., and Franca L.P. A new finite element formulation for computational fluid dynamics: VII. The Stokes problem with various well posed boundary conditions: Symmetric formulations that converge for all velocity/pressure spaces. Comput. Methods Appl. Mech. Engrg. 65 (1987) 86-96
    • (1987) Comput. Methods Appl. Mech. Engrg. , vol.65 , pp. 86-96
    • Hughes, T.J.R.1    Franca, L.P.2
  • 30
    • 22144493785 scopus 로고    scopus 로고
    • Relationships among some locally conservative discretization methods which handle discontinuous coefficients
    • Klausen R.A., and Russell T.F. Relationships among some locally conservative discretization methods which handle discontinuous coefficients. Comput. Geosci. 8 4 (2004) 341-377
    • (2004) Comput. Geosci. , vol.8 , Issue.4 , pp. 341-377
    • Klausen, R.A.1    Russell, T.F.2
  • 31
    • 2042421493 scopus 로고    scopus 로고
    • Finite volume/element discretization on unstructured meshes of the multiscale formulation of the large eddy simulation method and application to vortex shedding
    • Koobus B., and Farhat C. Finite volume/element discretization on unstructured meshes of the multiscale formulation of the large eddy simulation method and application to vortex shedding. Comput. Methods Appl. Mech. Engrg. 193 15-16 (2004) 1367-1383
    • (2004) Comput. Methods Appl. Mech. Engrg. , vol.193 , Issue.15-16 , pp. 1367-1383
    • Koobus, B.1    Farhat, C.2
  • 32
    • 2442475431 scopus 로고    scopus 로고
    • Local discontinuous Galerkin methods for nonlinear dispersive equations
    • Levy D., Shu C.W., and Yan J. Local discontinuous Galerkin methods for nonlinear dispersive equations. J. Comput. Phys. 196 (2004) 751-772
    • (2004) J. Comput. Phys. , vol.196 , pp. 751-772
    • Levy, D.1    Shu, C.W.2    Yan, J.3
  • 33
    • 0037200458 scopus 로고    scopus 로고
    • A stabilized mixed finite element method for Darcy flow
    • Masud A., and Hughes T.J.R. A stabilized mixed finite element method for Darcy flow. Comput. Methods Appl. Mech. Engrg. 191 39-40 (2002) 4341-4370
    • (2002) Comput. Methods Appl. Mech. Engrg. , vol.191 , Issue.39-40 , pp. 4341-4370
    • Masud, A.1    Hughes, T.J.R.2
  • 34
    • 1842636700 scopus 로고    scopus 로고
    • A multiscale/stabilized finite element method for the advection-diffusion equation
    • Masud A., and Khurram R. A multiscale/stabilized finite element method for the advection-diffusion equation. Comput. Methods Appl. Mech. Engrg. 193 (2004) 1997-2018
    • (2004) Comput. Methods Appl. Mech. Engrg. , vol.193 , pp. 1997-2018
    • Masud, A.1    Khurram, R.2
  • 35
    • 77956696042 scopus 로고    scopus 로고
    • Shape functions for three-dimensional control-volume mixed finite element methods on irregular grids
    • Hassanizadeh S.M., et al. (Ed), Elsevier, Amsterdam
    • 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
    • (2002) Computational Methods in Water Resources , vol.1 , pp. 359-366
    • Naff, R.F.1    Russell, T.F.2    Wilson, J.D.3
  • 37
    • 5144223344 scopus 로고    scopus 로고
    • A feasibility study for discontinuous Galerkin discretization with embedded Dirichlet boundary condition
    • Raalte M.H.V. A feasibility study for discontinuous Galerkin discretization with embedded Dirichlet boundary condition. Appl. Numer. Math. 51 (2004) 361-383
    • (2004) Appl. Numer. Math. , vol.51 , pp. 361-383
    • Raalte, M.H.V.1
  • 38
    • 0001175293 scopus 로고
    • A mixed finite element method for second order elliptic problems
    • Mathematical Aspects of the Finite Element Method. Galligani I., and Magenes E. (Eds), Springer-Verlag, New York
    • Raviart P.A., and Thomas J.M. A mixed finite element method for second order elliptic problems. In: Galligani I., and Magenes E. (Eds). Mathematical Aspects of the Finite Element Method. Lecture Notes in Mathematics vol. 606 (1977), Springer-Verlag, New York
    • (1977) Lecture Notes in Mathematics , vol.606
    • Raviart, P.A.1    Thomas, J.M.2
  • 39
    • 2042465004 scopus 로고    scopus 로고
    • Enhanced-discretization space time technique
    • Tezduyar T., and Sathe S. Enhanced-discretization space time technique. Comput. Methods Appl. Mech. Engrg. 193 15-16 (2004) 1385-1401
    • (2004) Comput. Methods Appl. Mech. Engrg. , vol.193 , Issue.15-16 , pp. 1385-1401
    • Tezduyar, T.1    Sathe, S.2
  • 40
    • 33645918200 scopus 로고    scopus 로고
    • J. Wan, Stabilized finite element methods for coupled geomechanics and multiphase flow, Ph.D. thesis, Stanford University, 2002 (Chapter 5).
  • 41
    • 3142713775 scopus 로고    scopus 로고
    • A discontinuous Galerkin formulation for a strain gradient-dependent damage model
    • Wells G.N., Garikipati K., and Molari L. A discontinuous Galerkin formulation for a strain gradient-dependent damage model. Comput. Methods Appl. Mech. Engrg. 193 (2004) 3633-3645
    • (2004) Comput. Methods Appl. Mech. Engrg. , vol.193 , pp. 3633-3645
    • Wells, G.N.1    Garikipati, K.2    Molari, L.3


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