메뉴 건너뛰기




Volumn 79, Issue 272, 2010, Pages 1915-1955

A new multiscale finite element method for high-contrast elliptic interface problems

Author keywords

Convergence; High contrast; Interfaces; Multiscale finite elements; Non periodic media; Second order elliptic problems

Indexed keywords


EID: 77956605824     PISSN: 00255718     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0025-5718-2010-02372-5     Document Type: Article
Times cited : (202)

References (45)
  • 1
    • 0037246341 scopus 로고    scopus 로고
    • The immersed interface/multigrid methods for interface problems
    • L. Adams, Z.L. Li, The immersed interface/multigrid methods for interface problems, SIAM J. Sci. Comput. 24 (2002), 463-479.
    • (2002) SIAM J. Sci. Comput. , vol.24 , pp. 463-479
    • Adams, L.1    Li, Z.L.2
  • 2
    • 29144440979 scopus 로고    scopus 로고
    • Robust a posteriori error estimation for nonconforming finite element approximation
    • M. Ainsworth, Robust a posteriori error estimation for nonconforming finite element approximation, SIAM J. Numer. Anal. 42 (2005), 2320-2341.
    • (2005) SIAM J. Numer. Anal. , vol.42 , pp. 2320-2341
    • Ainsworth, M.1
  • 3
    • 0000024779 scopus 로고
    • The finite element method for elliptic equations with discontinuous coefficients
    • I. Babuška, The finite element method for elliptic equations with discontinuous coefficients, Computing 5 (1970), 207-213.
    • (1970) Computing , vol.5 , pp. 207-213
    • Babuška, I.1
  • 4
    • 0028483749 scopus 로고
    • Special finite element methods for a class of second order elliptic problems with rough coefficients
    • I. Babuška, G. Caloz, and J.E. Osborn, Special finite element methods for a class of second order elliptic problems with rough coefficients, SIAM J. Numer. Anal. 31 (1994), 945-981.
    • (1994) SIAM J. Numer. Anal. , vol.31 , pp. 945-981
    • Babuška, I.1    Caloz, G.2    Osborn, J.E.3
  • 5
    • 0000828256 scopus 로고
    • Generalized finite element methods: Their performance and their relation to mixed methods
    • I. Babuška and J.E. Osborn. Generalized finite element methods: Their performance and their relation to mixed methods, SIAM J. Numer. Anal. 20 (1983), 510-536.
    • (1983) SIAM J. Numer. Anal. , vol.20 , pp. 510-536
    • Babuška, I.1    Osborn, J.E.2
  • 6
    • 0011914559 scopus 로고
    • Fitted and unfitted finite element methods for elliptic-equations with smooth interfaces
    • J.W. Barrett and C.M. Elliott, Fitted and unfitted finite element methods for elliptic-equations with smooth interfaces, IMA J. Numer. Anal. 7 (1987), 283-300.
    • (1987) IMA J. Numer. Anal. , vol.7 , pp. 283-300
    • Barrett, J.W.1    Elliott, C.M.2
  • 7
    • 0039608629 scopus 로고    scopus 로고
    • Adaptive finite element methods for elliptic equations with non-smooth coefficients
    • C. Bernardi and R. Verfürth, Adaptive finite element methods for elliptic equations with non-smooth coefficients, Numer. Math. 85 (2000), 579-608.
    • (2000) Numer. Math. , vol.85 , pp. 579-608
    • Bernardi, C.1    Verfürth, R.2
  • 8
    • 34547506442 scopus 로고    scopus 로고
    • A coupling interface method for elliptic interface problems
    • I.-L. Chern and Y.-C. Shu, A coupling interface method for elliptic interface problems, J. Comput. Phys. 225 (2007), 2138-2174.
    • (2007) J. Comput. Phys. , vol.225 , pp. 2138-2174
    • Chern, I.-L.1    Shu, Y.-C.2
  • 9
    • 0032396367 scopus 로고    scopus 로고
    • Finite element methods and their convergence for elliptic and parabolic interface problems
    • Z. Chen and J. Zou, Finite element methods and their convergence for elliptic and parabolic interface problems, Numer. Math. 79 (1998), 175-202.
    • (1998) Numer. Math. , vol.79 , pp. 175-202
    • Chen, Z.1    Zou, J.2
  • 10
    • 84904154533 scopus 로고    scopus 로고
    • On discontinuous Galerkin methods for elliptic problems with discontinuous coefficients
    • M. Dryja, On discontinuous Galerkin methods for elliptic problems with discontinuous coefficients, Computational Methods in Applied Mathematics 3 (2003), 76-85.
    • (2003) Computational Methods in Applied Mathematics , vol.3 , pp. 76-85
    • Dryja, M.1
  • 11
    • 1842511702 scopus 로고    scopus 로고
    • An immersed interface method for solving anisotropic elliptic boundary value problems in three dimensions
    • M.A. Dumett and J.P. Keener, An immersed interface method for solving anisotropic elliptic boundary value problems in three dimensions, SIAM J. Sci. Comput. 25 (2003), 348-367.
    • (2003) SIAM J. Sci. Comput. , vol.25 , pp. 348-367
    • Dumett, M.A.1    Keener, J.P.2
  • 13
    • 0346837922 scopus 로고    scopus 로고
    • A non-oscillatory Eulerian approach to interfaces in multimaterial flows (the ghost fluid method)
    • R.P. Fedkiw, T. Aslam, B, Merriman and S. Osher, A non-oscillatory Eulerian approach to interfaces in multimaterial flows (the ghost fluid method), J. Comput. Phys. 152 (1999), 457-492.
    • (1999) J. Comput. Phys. , vol.152 , pp. 457-492
    • Fedkiw, R.P.1    Aslam, T.2    Merriman, B.3    Osher, S.4
  • 15
    • 34249880401 scopus 로고    scopus 로고
    • Domain decomposition for multiscale PDEs
    • I.G. Graham, P. Lechner and R. Scheichl, Domain decomposition for multiscale PDEs, Numer. Math. 106 (2007), 589-626.
    • (2007) Numer. Math. , vol.106 , pp. 589-626
    • Graham, I.G.1    Lechner, P.2    Scheichl, R.3
  • 18
    • 0031185285 scopus 로고    scopus 로고
    • A hybrid method for moving interface problems with application to the Hele-Shaw flow
    • T.Y. Hou, Z.L. Li, S. Osher and H. Zhao, A hybrid method for moving interface problems with application to the Hele-Shaw flow, J. Comp. Phys. 134 (1997), 236-252.
    • (1997) J. Comp. Phys. , vol.134 , pp. 236-252
    • Hou, T.Y.1    Li, Z.L.2    Osher, S.3    Zhao, H.4
  • 19
    • 0031161210 scopus 로고    scopus 로고
    • A multiscale finite element method for elliptic problems in composite materials and porous media
    • T.Y. Hou and X.-H. Wu, A multiscale finite element method for elliptic problems in composite materials and porous media, J. Comp. Phys. 134 (1997), 169-189.
    • (1997) J. Comp. Phys. , vol.134 , pp. 169-189
    • Hou, T.Y.1    Wu, X.-H.2
  • 20
    • 0039982148 scopus 로고    scopus 로고
    • Convergence of a multiscale finite element method for elliptic problems with rapidly oscillating coefficients
    • T.Y. Hou, X.-H. Wu and Z. Cai, Convergence of a multiscale finite element method for elliptic problems with rapidly oscillating coefficients, Math. Comp. 68 (1999), 913-943.
    • (1999) Math. Comp. , vol.68 , pp. 913-943
    • Hou, T.Y.1    Wu, X.-H.2    Cai, Z.3
  • 21
    • 0037144961 scopus 로고    scopus 로고
    • Some new a priori estimates for second-order elliptic and parabolic interface problems
    • J. Huang and J. Zou, Some new a priori estimates for second-order elliptic and parabolic interface problems, Journal of Differential Equations 184 (2002), 570-586.
    • (2002) Journal of Differential Equations , vol.184 , pp. 570-586
    • Huang, J.1    Zou, J.2
  • 22
    • 14544308369 scopus 로고    scopus 로고
    • The ghost fluid method for compressible gas-water simulation
    • B.C. Khoo, T.G. Liu and C.W. Wang, The ghost fluid method for compressible gas-water simulation, J. Comput. Phys. 204 (2005), 193-221.
    • (2005) J. Comput. Phys. , vol.204 , pp. 193-221
    • Khoo, B.C.1    Liu, T.G.2    Wang, C.W.3
  • 23
    • 0141850275 scopus 로고    scopus 로고
    • Ghost fluid method for strong shock impacting on material interface
    • B.C. Khoo, T.G. Liu and K.S. Yeo, Ghost fluid method for strong shock impacting on material interface, J. Comput. Phys. 190 (2003), 651-681.
    • (2003) J. Comput. Phys. , vol.190 , pp. 651-681
    • Khoo, B.C.1    Liu, T.G.2    Yeo, K.S.3
  • 24
    • 0028485385 scopus 로고
    • The immersed interface method for elliptic equations with discontinuous coefficients and singular sources
    • R.J. LeVeque and Z.L. Li, The immersed interface method for elliptic equations with discontinuous coefficients and singular sources, SIAM J. Numer. Anal. 31 (1994), 1019-1044.
    • (1994) SIAM J. Numer. Anal. , vol.31 , pp. 1019-1044
    • Leveque, R.J.1    Li, Z.L.2
  • 25
    • 85190571330 scopus 로고    scopus 로고
    • Optimal a priori estimates for higher order finite element methods for elliptic interface problems
    • (in press)
    • J. Li, J.M. Melenk, B. Wohlmuth and J. Zou, Optimal a priori estimates for higher order finite element methods for elliptic interface problems, Applied Numerical Mathematics (in press) (2009).
    • (2009) Applied Numerical Mathematics
    • Li, J.1    Melenk, J.M.2    Wohlmuth, B.3    Zou, J.4
  • 26
    • 0000641836 scopus 로고    scopus 로고
    • A fast iterative algorithm for elliptic interface problems
    • Z.L. Li, A fast iterative algorithm for elliptic interface problems, SIAM J. Numer. Anal. 35 (1998), 230-254.
    • (1998) SIAM J. Numer. Anal. , vol.35 , pp. 230-254
    • Li, Z.L.1
  • 27
    • 0036208213 scopus 로고    scopus 로고
    • Maximum principle preserving schemes for interface problems with discontinuous coefficients
    • Z.L. Li and K. Ito, Maximum principle preserving schemes for interface problems with discontinuous coefficients, SIAM J. Sci. Comput. 23 (2001), 339-361.
    • (2001) SIAM J. Sci. Comput. , vol.23 , pp. 339-361
    • Li, Z.L.1    Ito, K.2
  • 28
    • 0742271742 scopus 로고    scopus 로고
    • New Cartesian grid methods for interface problems using the finite element formulation
    • Z.L. Li, T. Lin and X. Wu, New Cartesian grid methods for interface problems using the finite element formulation, Numer. Math. 96 (2003), 61-98.
    • (2003) Numer. Math. , vol.96 , pp. 61-98
    • Li, Z.L.1    Lin, T.2    Wu, X.3
  • 30
    • 0001491689 scopus 로고    scopus 로고
    • A boundary condition capturing method for Poisson's equation on irregular domains
    • X.D. Liu, R.P. Fedkiw and M.J. Kang, A boundary condition capturing method for Poisson's equation on irregular domains, J. Comput. Phys. 160 (2000), 151-178.
    • (2000) J. Comput. Phys. , vol.160 , pp. 151-178
    • Liu, X.D.1    Fedkiw, R.P.2    Kang, M.J.3
  • 31
    • 0141872535 scopus 로고    scopus 로고
    • Convergence of the ghost fluid method for elliptic equations with interfaces
    • X.D. Liu and T. C. Sideris, Convergence of the ghost fluid method for elliptic equations with interfaces, Math. Comput. 72 (2003), 1731-1746.
    • (2003) Math. Comput. , vol.72 , pp. 1731-1746
    • Liu, X.D.1    Sideris, T.C.2
  • 32
    • 0000369989 scopus 로고    scopus 로고
    • The layer potential technique for the inverse conductivity problem
    • H. Kang and J.K. Seo, The layer potential technique for the inverse conductivity problem, Inverse Problems 12 (1996) 267-278.
    • (1996) Inverse Problems , vol.12 , pp. 267-278
    • Kang, H.1    Seo, J.K.2
  • 33
    • 0001495158 scopus 로고    scopus 로고
    • Numerical identification of discontinuous conductivity coefficients
    • H. Kang, J.K. Seo and D. Sheen, Numerical identification of discontinuous conductivity coefficients, Inverse Problems 13 (1997) 113-123.
    • (1997) Inverse Problems , vol.13 , pp. 113-123
    • Kang, H.1    Seo, J.K.2    Sheen, D.3
  • 36
    • 56549129453 scopus 로고    scopus 로고
    • Analysis of FETI methods for multiscale PDEs
    • C. Pechstein and R. Scheichl, Analysis of FETI methods for multiscale PDEs, Numer. Math. 111 (2008), 293-333.
    • (2008) Numer. Math. , vol.111 , pp. 293-333
    • Pechstein, C.1    Scheichl, R.2
  • 37
    • 0017424014 scopus 로고
    • Numerical study of blood flow in the heart
    • C.S. Peskin, Numerical study of blood flow in the heart, J. Comput. Phys. 25 (1977), 220-252.
    • (1977) J. Comput. Phys. , vol.25 , pp. 220-252
    • Peskin, C.S.1
  • 38
    • 33751544551 scopus 로고    scopus 로고
    • The immersed boundary method
    • C.S. Peskin, The immersed boundary method, Acta Numerica 11 (2002), 479-517.
    • (2002) Acta Numerica , vol.11 , pp. 479-517
    • Peskin, C.S.1
  • 39
    • 0242308001 scopus 로고    scopus 로고
    • Optimal a priori estimates for interface problems
    • M. Plum and C. Wieners, Optimal a priori estimates for interface problems, Numer. Math. 95 (2003), 735-759.
    • (2003) Numer. Math. , vol.95 , pp. 735-759
    • Plum, M.1    Wieners, C.2
  • 42
    • 3242694679 scopus 로고
    • A front-tracking method for viscous, incompressible, multi-fluid flows
    • S.O. Unverdi and G. Tryggvason, A front-tracking method for viscous, incompressible, multi-fluid flows, J. Comput. Phys. 100 (1992), 25-37.
    • (1992) J. Comput. Phys. , vol.100 , pp. 25-37
    • Unverdi, S.O.1    Tryggvason, G.2
  • 45
    • 31744448526 scopus 로고    scopus 로고
    • High order matched interface and boundary method for elliptic equations with discontinuous coefficients and singular sources
    • Y.C. Zhou, S. Zhao, M. Feig and G.W. Wei, High order matched interface and boundary method for elliptic equations with discontinuous coefficients and singular sources, J. Comp. Phys. 213 (2006), 1-30.
    • (2006) J. Comp. Phys. , vol.213 , pp. 1-30
    • Zhou, Y.C.1    Zhao, S.2    Feig, M.3    Wei, G.W.4


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.