메뉴 건너뛰기




Volumn 24, Issue 1, 2008, Pages 60-78

A stabilized method for a secondary consolidation Biot's model

Author keywords

Finite differences; Poroelasticity; Secondary consolidation; Stabilized methods; Staggered grids

Indexed keywords


EID: 38049120168     PISSN: 0749159X     EISSN: 10982426     Source Type: Journal    
DOI: 10.1002/num.20242     Document Type: Article
Times cited : (16)

References (21)
  • 1
    • 0003430263 scopus 로고
    • Theoretical soil mechanics
    • 1 K. Terzaghi, Theoretical soil mechanics, Wiley, New York, 1943.
    • (1943)
    • Terzaghi, K.1
  • 2
    • 0345643551 scopus 로고
    • General theory of three dimensional consolidation
    • 2 M. Biot, General theory of three dimensional consolidation, J Appl Phys 12 ( 1941), 155–169.
    • (1941) J Appl Phys , vol.12 , pp. 155-169
    • Biot, M.1
  • 3
    • 0001516947 scopus 로고    scopus 로고
    • Multiscale flow and deformation in hydrophilic swelling porous media
    • 3 M. A. Murad and J. H. Cushman, Multiscale flow and deformation in hydrophilic swelling porous media, Int J Eng Sci 3 ( 1996), 313–338.
    • (1996) Int J Eng Sci , vol.3 , pp. 313-338
    • Murad, M.A.1    Cushman, J.H.2
  • 4
    • 4544264386 scopus 로고    scopus 로고
    • Diffusion in deforming porous media
    • 4 R. E. Showalter, Diffusion in deforming porous media, Math Anal 10 ( 2003), 661–678.
    • (2003) Math Anal , vol.10 , pp. 661-678
    • Showalter, R.E.1
  • 6
    • 0034311246 scopus 로고    scopus 로고
    • Diffusion in poroelastic media
    • 6 R. E. Showalter, Diffusion in poroelastic media, J Math Anal Appl 251 ( 2000), 310–340.
    • (2000) J Math Anal Appl , vol.251 , pp. 310-340
    • Showalter, R.E.1
  • 7
    • 0003433073 scopus 로고    scopus 로고
    • The finite element method in the static and dynamic deformation and consolidation of porous media
    • 7 R. W. Lewis and B. A. Schrefler, The finite element method in the static and dynamic deformation and consolidation of porous media, Wiley, Chichester, 1998.
    • (1998)
    • Lewis, R.W.1    Schrefler, B.A.2
  • 8
    • 0016093926 scopus 로고
    • On the existence, uniqueness and approximation of saddle‐point problems arising from Lagrange multipliers
    • 8 F. Brezzi, On the existence, uniqueness and approximation of saddle‐point problems arising from Lagrange multipliers, RAIRO Model Math Anal Numer 8 ( 1974), 129–151.
    • (1974) RAIRO Model Math Anal Numer , vol.8 , pp. 129-151
    • Brezzi, F.1
  • 9
    • 0026835573 scopus 로고
    • Improved accuracy in finite element analysis of Biot's consolidation problem
    • 9 M. A. Murad and A. F. D. Loula, Improved accuracy in finite element analysis of Biot's consolidation problem, Comput Methods Appl Mech Eng 95 ( 1992), 359–382.
    • (1992) Comput Methods Appl Mech Eng , vol.95 , pp. 359-382
    • Murad, M.A.1    Loula, A.F.D.2
  • 10
    • 0028381470 scopus 로고
    • On stability and convergence of finite element approximations of Biot's consolidation problem
    • 10 M. A. Murad and A. F. D. Loula, On stability and convergence of finite element approximations of Biot's consolidation problem, Int J Numer Methods Eng 37 ( 1994), 645–667.
    • (1994) Int J Numer Methods Eng , vol.37 , pp. 645-667
    • Murad, M.A.1    Loula, A.F.D.2
  • 11
    • 0000036606 scopus 로고    scopus 로고
    • Asymptotic behaviour of semidiscrete finite‐element approximations of Biot's consolidation problem
    • 11 M. A. Murad, V. Thomée, and A. F. D. Loula, Asymptotic behaviour of semidiscrete finite‐element approximations of Biot's consolidation problem, SIAM J Numer Anal 33 ( 1996), 1065–1083.
    • (1996) SIAM J Numer Anal , vol.33 , pp. 1065-1083
    • Murad, M.A.1    Thomée, V.2    Loula, A.F.D.3
  • 12
    • 0141796472 scopus 로고    scopus 로고
    • A new stabilized enhanced strain element with equal order of interpolation for soil consolidation problems
    • 12 P. Mira, M. Pastor, T. Li, and X. Liu, A new stabilized enhanced strain element with equal order of interpolation for soil consolidation problems, Comput Methods Appl Mech Eng 192 ( 2003), 4257–4277.
    • (2003) Comput Methods Appl Mech Eng , vol.192 , pp. 4257-4277
    • Mira, P.1    Pastor, M.2    Li, T.3    Liu, X.4
  • 13
    • 0037352983 scopus 로고    scopus 로고
    • A finite difference analysis of Biot's consolidation model
    • 13 F. J. Gaspar, F. J. Lisbona, and P. N. Vabishchevich, A finite difference analysis of Biot's consolidation model, Appl Numer Math 44 ( 2003), 487–506.
    • (2003) Appl Numer Math , vol.44 , pp. 487-506
    • Gaspar, F.J.1    Lisbona, F.J.2    Vabishchevich, P.N.3
  • 14
    • 28444440957 scopus 로고    scopus 로고
    • Finite element analysis of poro‐elastic consolidation in porous media: standard and mixed approaches
    • 14 J. Korsawe, G. Starke, W. Wang, and O. Kolditz, Finite element analysis of poro‐elastic consolidation in porous media: standard and mixed approaches, Comput Methods Appl Mech Eng 195 ( 2006), 1096–1115.
    • (2006) Comput Methods Appl Mech Eng , vol.195 , pp. 1096-1115
    • Korsawe, J.1    Starke, G.2    Wang, W.3    Kolditz, O.4
  • 15
    • 33645988819 scopus 로고    scopus 로고
    • Staggered grid discretizations for the quasistatic Biot's consolidation problem
    • 15 F. J. Gaspar, F. J. Lisbona, and P. N. Vabishchevich, Staggered grid discretizations for the quasistatic Biot's consolidation problem, Appl Numer Math 56 ( 2006), 888–898.
    • (2006) Appl Numer Math , vol.56 , pp. 888-898
    • Gaspar, F.J.1    Lisbona, F.J.2    Vabishchevich, P.N.3
  • 16
    • 33751075445 scopus 로고    scopus 로고
    • An efficient multigrid solver for a reformulated version of the poroelasticity system
    • 16 F. J. Gaspar, F. J. Lisbona, C. W. Oosterlee, and P. N. Vabishchevich, An efficient multigrid solver for a reformulated version of the poroelasticity system, Comput Methods Appl Mech Eng 196 ( 2007), 1447–1457.
    • (2007) Comput Methods Appl Mech Eng , vol.196 , pp. 1447-1457
    • Gaspar, F.J.1    Lisbona, F.J.2    Oosterlee, C.W.3    Vabishchevich, P.N.4
  • 17
    • 85120587070 scopus 로고    scopus 로고
    • A stabilized difference scheme for deformable porous media and its numerical resolution by multigrid methods
    • 17 F. J. Gaspar, F. J. Lisbona, and C. W. Oosterlee, A stabilized difference scheme for deformable porous media and its numerical resolution by multigrid methods, Comput Vis Sci, to appear.
    • Comput Vis Sci
    • Gaspar, F.J.1    Lisbona, F.J.2    Oosterlee, C.W.3
  • 18
    • 0003731729 scopus 로고    scopus 로고
    • Conservative finite‐difference methods on general grids
    • 18 M. Shashkov, Conservative finite‐difference methods on general grids, CRC Press, Boca Raton, Florida, 1996.
    • (1996)
    • Shashkov, M.1
  • 19
    • 35448959458 scopus 로고    scopus 로고
    • Finite‐difference approximation of mathematical physics problems on irregular grids
    • 19 P. N. Vabishchevich, Finite‐difference approximation of mathematical physics problems on irregular grids, Comput Meth Appl Math 5 ( 2005), 294–330.
    • (2005) Comput Meth Appl Math , vol.5 , pp. 294-330
    • Vabishchevich, P.N.1
  • 20
    • 10044270001 scopus 로고    scopus 로고
    • Systematic comparison of coupled and distributive smoothing in multigrid for the poroelasticity system
    • 20 F. J. Gaspar, F. J. Lisbona, C. W. Oosterlee, and R. A. Wienands, Systematic comparison of coupled and distributive smoothing in multigrid for the poroelasticity system, Numer Lin Algebra Appl 11 ( 2004), 93–113.
    • (2004) Numer Lin Algebra Appl , vol.11 , pp. 93-113
    • Gaspar, F.J.1    Lisbona, F.J.2    Oosterlee, C.W.3    Wienands, R.A.4
  • 21
    • 7544233092 scopus 로고    scopus 로고
    • An efficient multigrid solver based on distributive smoothing for poroelasticity equations
    • 21 R. Wienands, F. J. Gaspar, F. J. Lisbona, and C. W. Oosterlee, An efficient multigrid solver based on distributive smoothing for poroelasticity equations, Computing 73 ( 2004), 99–119.
    • (2004) Computing , vol.73 , pp. 99-119
    • Wienands, R.1    Gaspar, F.J.2    Lisbona, F.J.3    Oosterlee, C.W.4


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.