메뉴 건너뛰기




Volumn 57, Issue 4, 2007, Pages 383-401

Fully implicit discontinuous finite element methods for two-phase flow

Author keywords

h and p version; Heterogeneous media; Newton Raphson; Nonsymmetric interior penalty Galerkin; Quarter five spot

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; FINITE ELEMENT METHOD; GALERKIN METHODS; POLYNOMIALS; POROUS MATERIALS; ROBUSTNESS (CONTROL SYSTEMS);

EID: 33847260775     PISSN: 01689274     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.apnum.2006.04.004     Document Type: Article
Times cited : (87)

References (28)
  • 1
    • 0001163226 scopus 로고
    • An interior penalty finite element method with discontinuous elements
    • Arnold D.N. An interior penalty finite element method with discontinuous elements. SIAM Journal on Numerical Analysis 19 (1982) 742-760
    • (1982) SIAM Journal on Numerical Analysis , vol.19 , pp. 742-760
    • Arnold, D.N.1
  • 3
    • 33847252035 scopus 로고    scopus 로고
    • P. Bastian, B. Rivière, Discontinuous Galerkin methods for two-phase flow in porous media, Technical Report 2004-28, University of Heidelberg, 2004
  • 4
  • 5
    • 0003325193 scopus 로고
    • Mathematical Models and Finite Elements for Reservoir Simulation
    • Elsevier, Amsterdam
    • Chavent G., and Jaffré J. Mathematical Models and Finite Elements for Reservoir Simulation. Studies in Mathematics and its Applications (1986), Elsevier, Amsterdam
    • (1986) Studies in Mathematics and its Applications
    • Chavent, G.1    Jaffré, J.2
  • 6
    • 0344393366 scopus 로고    scopus 로고
    • The local discontinuous Galerkin method for convection-diffusion systems
    • Cockburn B., and Shu C.-W. The local discontinuous Galerkin method for convection-diffusion systems. SIAM Journal on Numerical Analysis 35 (1998) 2440-2463
    • (1998) SIAM Journal on Numerical Analysis , vol.35 , pp. 2440-2463
    • Cockburn, B.1    Shu, C.-W.2
  • 7
    • 84966246413 scopus 로고
    • TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservative laws II: General framework
    • Cockburn B., and Shu C.W. TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservative laws II: General framework. Mathematics of Computation 52 (1989) 411-435
    • (1989) Mathematics of Computation , vol.52 , pp. 411-435
    • Cockburn, B.1    Shu, C.W.2
  • 8
    • 33745852637 scopus 로고    scopus 로고
    • Y. Epshteyn, B. Rivière, On the solution of incompressible two-phase flow by a p-version discontinuous Galerkin method, Communications in Numerical Methods in Engineering (2006), in press
  • 9
    • 33847284049 scopus 로고    scopus 로고
    • O. Eslinger, Discontinuous Galerkin finite element methods applied to two-phase, air-water flow problems, PhD thesis, The University of Texas at Austin, 2005
  • 10
    • 0000370771 scopus 로고
    • A control volume finite element approach to NAPL groundwater contamination
    • Forsyth P.A. A control volume finite element approach to NAPL groundwater contamination. SIAM Journal on Scientific and Statistical Computing 12 (1991) 1029-1057
    • (1991) SIAM Journal on Scientific and Statistical Computing , vol.12 , pp. 1029-1057
    • Forsyth, P.A.1
  • 13
    • 0036556363 scopus 로고    scopus 로고
    • Discontinuous hp-finite element methods for advection-diffusion reaction problems
    • Houston P., Schwab C., and Süli E. Discontinuous hp-finite element methods for advection-diffusion reaction problems. SIAM Journal on Numerical Analysis 39 6 (2002) 2133-2163
    • (2002) SIAM Journal on Numerical Analysis , vol.39 , Issue.6 , pp. 2133-2163
    • Houston, P.1    Schwab, C.2    Süli, E.3
  • 14
    • 0033617077 scopus 로고    scopus 로고
    • Multiphase flow in heterogeneous porous media: a classical finite element method versus and implicit pressure-explicit saturation-based mixed finite element-finite volume approach
    • Huber R., and Helmig R. Multiphase flow in heterogeneous porous media: a classical finite element method versus and implicit pressure-explicit saturation-based mixed finite element-finite volume approach. International Journal for Numerical Methods in Fluids 29 (1999) 899-920
    • (1999) International Journal for Numerical Methods in Fluids , vol.29 , pp. 899-920
    • Huber, R.1    Helmig, R.2
  • 15
    • 33846524895 scopus 로고    scopus 로고
    • W. Klieber, B. Rivière, Adaptive simulations of two-phase flow by discontinuous Galerkin methods, Computer Methods in Applied Mechanics and Engineering (2006), in press
  • 16
    • 0348006695 scopus 로고    scopus 로고
    • A finite volume scheme for the simulation of two-phase incompressible flow in porous media
    • Michel A. A finite volume scheme for the simulation of two-phase incompressible flow in porous media. SIAM Journal on Numerical Analysis 41 (2003) 1301-1317
    • (2003) SIAM Journal on Numerical Analysis , vol.41 , pp. 1301-1317
    • Michel, A.1
  • 17
    • 0032022066 scopus 로고    scopus 로고
    • Multiphase flow and transport modeling in heterogeneous porous media: Challenges and approaches
    • Miller C.T., Christakos G., Imhoff P.T., McBride J.F., and Pedit J.A. Multiphase flow and transport modeling in heterogeneous porous media: Challenges and approaches. Advances in Water Resources 21 2 (1998) 77-120
    • (1998) Advances in Water Resources , vol.21 , Issue.2 , pp. 77-120
    • Miller, C.T.1    Christakos, G.2    Imhoff, P.T.3    McBride, J.F.4    Pedit, J.A.5
  • 18
    • 2542557493 scopus 로고    scopus 로고
    • Modelling two-phase incompressible flow in porous media using mixed hybrid and discontinuous finite elements
    • Nayagum D., Schäfer G., and Mosé R. Modelling two-phase incompressible flow in porous media using mixed hybrid and discontinuous finite elements. Computational Geosciences 8 1 (2004) 49-73
    • (2004) Computational Geosciences , vol.8 , Issue.1 , pp. 49-73
    • Nayagum, D.1    Schäfer, G.2    Mosé, R.3
  • 22
    • 84893462046 scopus 로고    scopus 로고
    • B. Rivière, Numerical study of a discontinuous Galerkin method for incompressible two-phase flow, in: Proceedings of ECCOMAS 2004 (CD-ROM), vol. 2, Jyvaskyla, 2004
  • 26
    • 0343831462 scopus 로고    scopus 로고
    • Part II. Discontinuous Galerkin method applied to a single phase flow in porous media
    • Rivière B., Wheeler M.F., and Banas K. Part II. Discontinuous Galerkin method applied to a single phase flow in porous media. Computational Geosciences 4 (2000) 337-349
    • (2000) Computational Geosciences , vol.4 , pp. 337-349
    • Rivière, B.1    Wheeler, M.F.2    Banas, K.3
  • 27
    • 0033511173 scopus 로고    scopus 로고
    • Improved energy estimates for interior penalty, constrained and discontinuous Galerkin methods for elliptic problems. Part I
    • Rivière B., Wheeler M.F., and Girault V. Improved energy estimates for interior penalty, constrained and discontinuous Galerkin methods for elliptic problems. Part I. Computational Geosciences 3 (1999) 337-360
    • (1999) Computational Geosciences , vol.3 , pp. 337-360
    • Rivière, B.1    Wheeler, M.F.2    Girault, V.3
  • 28
    • 0000802762 scopus 로고
    • An elliptic collocation-finite element method with interior penalties
    • Wheeler M.F. An elliptic collocation-finite element method with interior penalties. SIAM Journal on Numerical Analysis 15 1 (1978) 152-161
    • (1978) SIAM Journal on Numerical Analysis , vol.15 , Issue.1 , pp. 152-161
    • Wheeler, M.F.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.