메뉴 건너뛰기




Volumn 43, Issue 2, 2009, Pages 353-375

A posteriori error analysis of Euler-Galerkin approximations to coupled elliptic-parabolic problems

Author keywords

a posteriori error analysis; Energy norm; Finite element method; Hydro mechanical coupling; Poroelasticity.

Indexed keywords


EID: 66249106368     PISSN: 0764583X     EISSN: 12903841     Source Type: Journal    
DOI: 10.1051/m2an:2008048     Document Type: Article
Times cited : (60)

References (26)
  • 1
    • 0035630248 scopus 로고    scopus 로고
    • On one approach to a posteriori error estimates for evolution problems solved by the method-of-lines
    • I. Babuška, M. Feistauer and P. Šolín, On one approach to a posteriori error estimates for evolution problems solved by the method-of-lines. Numer. Math. 89 (2001) 225-256.
    • (2001) Numer. Math , vol.89 , pp. 225-256
    • Babuška, I.1    Feistauer, M.2    Šolín, P.3
  • 2
    • 85022001969 scopus 로고    scopus 로고
    • An optimal control approach to a posteriori error estimation in finite element methods
    • R. Becker and R. Rannacher, An optimal control approach to a posteriori error estimation in finite element methods. Acta Numer. 10 (2001) 1-102.
    • (2001) Acta Numer , vol.10 , pp. 1-102
    • Becker, R.1    Rannacher, R.2
  • 3
    • 21644485033 scopus 로고    scopus 로고
    • A posteriori analysis of the finite element discretization of some parabolic equations
    • A. Bergam, C. Bernardi and Z. Mghazli, A posteriori analysis of the finite element discretization of some parabolic equations. Math. Comp. 74 (2005) 1117-1138.
    • (2005) Math. Comp , vol.74 , pp. 1117-1138
    • Bergam, A.1    Bernardi, C.2    Mghazli, Z.3
  • 4
    • 0345643551 scopus 로고
    • General theory of three-dimensional consolidation
    • M.A. 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.A.1
  • 6
    • 2942692259 scopus 로고    scopus 로고
    • An adaptive finite element algorithm with reliable and efficient error control for linear parabolic problems
    • Z. Chen and J. Feng, An adaptive finite element algorithm with reliable and efficient error control for linear parabolic problems. Math. Comp. 73 (2004) 1167-1193.
    • (2004) Math. Comp , vol.73 , pp. 1167-1193
    • Chen, Z.1    Feng, J.2
  • 7
    • 0016541865 scopus 로고
    • Approximation by finite element functions using local regularization
    • P. Clément, Approximation by finite element functions using local regularization. RAIRO Anal. Numér. 9 (1975) 77-84.
    • (1975) RAIRO Anal. Numér , vol.9 , pp. 77-84
    • Clément, P.1
  • 8
    • 0026106415 scopus 로고
    • Adaptive finite element methods for parabolic problems. I. A linear model problem
    • K. Eriksson and C. Johnson, Adaptive finite element methods for parabolic problems. I. A linear model problem. SIAM J. Numer. Anal. 28 (1991) 43-77.
    • (1991) SIAM J. Numer. Anal , vol.28 , pp. 43-77
    • Eriksson, K.1    Johnson, C.2
  • 11
    • 33750850308 scopus 로고    scopus 로고
    • Elliptic reconstruction and a posteriori error estimates for fully discrete linear parabolic problems
    • O. Lakkis and Ch. Makridakis, Elliptic reconstruction and a posteriori error estimates for fully discrete linear parabolic problems. Math. Comp. 75 (2006) 1627-1658.
    • (2006) Math. Comp , vol.75 , pp. 1627-1658
    • Lakkis, O.1    Makridakis, C.2
  • 12
    • 1342297216 scopus 로고    scopus 로고
    • Ellitpic reconstruction and a posteriori error estimates for elliptic problems
    • Ch. Makridakis and R.H. Nochetto, Ellitpic reconstruction and a posteriori error estimates for elliptic problems. SIAM J. Numer. Anal. 41 (2003) 1585-1594.
    • (2003) SIAM J. Numer. Anal , vol.41 , pp. 1585-1594
    • Makridakis, C.1    Nochetto, R.H.2
  • 14
    • 0026835573 scopus 로고
    • Improved accuracy in finite element analysis of Biot's consolidation problem
    • M.A. Murad and A.F.D. Loula, Improved accuracy in finite element analysis of Biot's consolidation problem. Comput. Meth. Appl. Mech. Engrg. 95 (1992) 359-382.
    • (1992) Comput. Meth. Appl. Mech. Engrg , vol.95 , pp. 359-382
    • Murad, M.A.1    Loula, A.F.D.2
  • 15
    • 0028381470 scopus 로고
    • On stability and convergence of finite element approximations of Biot's consolidation problem
    • M.A. Murad and A.F.D. Loula, On stability and convergence of finite element approximations of Biot's consolidation problem. Internat. J. Numer. Methods Engrg. 37 (1994) 645-667.
    • (1994) Internat. J. Numer. Methods Engrg , vol.37 , pp. 645-667
    • Murad, M.A.1    Loula, A.F.D.2
  • 16
    • 0000036606 scopus 로고    scopus 로고
    • Asymptotic behavior of semidiscrete finite-element approximations of Biot's consolidation problem
    • M.A. Murad, V. Thomée and A.F.D. Loula, Asymptotic behavior 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
  • 17
    • 0032308963 scopus 로고    scopus 로고
    • Adaptive finite elements for a linear parabolic problem
    • M. Picasso, Adaptive finite elements for a linear parabolic problem. Comput. Methods Appl. Mech. Engrg. 167 (1998) 223-237.
    • (1998) Comput. Methods Appl. Mech. Engrg , vol.167 , pp. 223-237
    • Picasso, M.1
  • 18
    • 84966200902 scopus 로고
    • Finite element interpolation of nonsmooth functions satisfying boundary conditions
    • R.L. Scott and S. Zhang, Finite element interpolation of nonsmooth functions satisfying boundary conditions. Math. Comp. 54 (1990) 483-493.
    • (1990) Math. Comp , vol.54 , pp. 483-493
    • Scott, R.L.1    Zhang, S.2
  • 20
    • 0034311246 scopus 로고    scopus 로고
    • Diffusion in poro-elastic media
    • R.E. Showalter, Diffusion in poro-elastic media. J. Math. Anal. Appl. 251 (2000) 310-340.
    • (2000) J. Math. Anal. Appl , vol.251 , pp. 310-340
    • Showalter, R.E.1
  • 22
    • 0028423814 scopus 로고
    • A posteriori error estimations and adaptative mesh-refinement techniques
    • R. Verfürth, A posteriori error estimations and adaptative mesh-refinement techniques. J. Comput. Appl. Math. 50 (1994) 67-83.
    • (1994) J. Comput. Appl. Math , vol.50 , pp. 67-83
    • Verfürth, R.1
  • 24
    • 10744223588 scopus 로고    scopus 로고
    • A posteriori error estimates for finite element discretizations of the heat equation
    • R. Verfürth, A posteriori error estimates for finite element discretizations of the heat equation. Calcolo 40 (2003) 195-212.
    • (2003) Calcolo , vol.40 , pp. 195-212
    • Verfürth, R.1
  • 26
    • 0001287713 scopus 로고
    • 2 error estimates for Galerkin approximations to parabolic partial differential equations
    • 2 error estimates for Galerkin approximations to parabolic partial differential equations. SIAM J. Numer. Anal. 10 (1973) 723-759.
    • (1973) SIAM J. Numer. Anal , vol.10 , pp. 723-759
    • Wheeler, M.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.