메뉴 건너뛰기




Volumn 16, Issue 2, 2006, Pages 275-297

Convergence of mimetic finite difference method for diffusion problems on polyhedral meshes with curved faces

Author keywords

Convergence; Finite differences; Mimetic discretizations; Polyhedral meshes

Indexed keywords


EID: 32644433326     PISSN: 02182025     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218202506001157     Document Type: Article
Times cited : (103)

References (19)
  • 1
    • 0036924061 scopus 로고    scopus 로고
    • An introduction to multipoint flux approximations for quadrilateral grids
    • I. Aavatsmark, An introduction to multipoint flux approximations for quadrilateral grids, Comp. Geosci. 6 (2002) 405-432.
    • (2002) Comp. Geosci. , vol.6 , pp. 405-432
    • Aavatsmark, I.1
  • 2
    • 0001163226 scopus 로고
    • An interior penalty finite element method with discontinuous elements
    • D. Arnold, An interior penalty finite element method with discontinuous elements, SIAM J. Numer. Anal. 19 (1982) 742-760.
    • (1982) SIAM J. Numer. Anal. , vol.19 , pp. 742-760
    • Arnold, D.1
  • 3
    • 0035708126 scopus 로고    scopus 로고
    • Convergence of mimetic finite difference discretizations of the diffusion equation
    • M. Berndt, K. Lipnikov, J. D. Moulton and M. Shashkov, Convergence of mimetic finite difference discretizations of the diffusion equation, East-West J. Numer. Math. 9 (2001) 253-284.
    • (2001) East-West J. Numer. Math. , vol.9 , pp. 253-284
    • Berndt, M.1    Lipnikov, K.2    Moulton, J.D.3    Shashkov, M.4
  • 4
    • 32644431624 scopus 로고    scopus 로고
    • Superconvergence of the velocity in mimetic finite difference methods on quadrilaterals
    • M. Berndt, K. Lipnikov, M. Shashkov, M. Wheeler and I. Yotov, Superconvergence of the velocity in mimetic finite difference methods on quadrilaterals, SIAM J. Numer. Anal. 43 (2005) 1728-1749.
    • (2005) SIAM J. Numer. Anal. , vol.43 , pp. 1728-1749
    • Berndt, M.1    Lipnikov, K.2    Shashkov, M.3    Wheeler, M.4    Yotov, I.5
  • 5
    • 0037354898 scopus 로고    scopus 로고
    • A proof of the inf-sup condition for the stokes equations on Lipschitz domains
    • J. H. Bramble, A proof of the inf-sup condition for the stokes equations on Lipschitz domains, Math. Mod. Meth. Appl. Sci. 3 (2003) 361-371.
    • (2003) Math. Mod. Meth. Appl. Sci. , vol.3 , pp. 361-371
    • Bramble, J.H.1
  • 8
    • 26944484259 scopus 로고    scopus 로고
    • Convergence of mimetic finite difference method for diffusion problems on polyhedral meshes
    • to appear
    • F. Brezzi, K. Lipnikov and M. Shashkov, Convergence of mimetic finite difference method for diffusion problems on polyhedral meshes, SIAM J. Numer. Anal., to appear.
    • SIAM J. Numer. Anal.
    • Brezzi, F.1    Lipnikov, K.2    Shashkov, M.3
  • 9
    • 25144443045 scopus 로고    scopus 로고
    • A family of mimetic finite difference methods on polygonal and polyhedral meshes
    • F. Brezzi, K. Lipnikov and V. Simoncini, A family of mimetic finite difference methods on polygonal and polyhedral meshes, Math. Mod. Meth. Appl. Sci. 15 (2005) 1533-1551.
    • (2005) Math. Mod. Meth. Appl. Sci. , vol.15 , pp. 1533-1551
    • Brezzi, F.1    Lipnikov, K.2    Simoncini, V.3
  • 10
    • 0035922232 scopus 로고    scopus 로고
    • A tensor artificial viscosity using a mimetic finite difference algorithm
    • J. Campbell and M. Shashkov, A tensor artificial viscosity using a mimetic finite difference algorithm, J. Comput. Phys. 172 (2001) 739-765.
    • (2001) J. Comput. Phys. , vol.172 , pp. 739-765
    • Campbell, J.1    Shashkov, M.2
  • 11
    • 84966242123 scopus 로고
    • Global estimates for mixed methods for second order elliptic equations
    • J. Douglas and J. Roberts, Global estimates for mixed methods for second order elliptic equations, Math. Comput. 44 (1985) 39-52.
    • (1985) Math. Comput. , vol.44 , pp. 39-52
    • Douglas, J.1    Roberts, J.2
  • 12
    • 0036923031 scopus 로고    scopus 로고
    • Mimetic finite difference methods for diffusion equations
    • J. Hyman, J. Morel, M. Shashkov and S. Steinberg, Mimetic finite difference methods for diffusion equations, Comp. Geosci. 6 (2002) 333-352.
    • (2002) Comp. Geosci. , vol.6 , pp. 333-352
    • Hyman, J.1    Morel, J.2    Shashkov, M.3    Steinberg, S.4
  • 13
    • 84875677944 scopus 로고    scopus 로고
    • Mimetic discretizations for Maxwell's equations and the equations of magnetic diffusion
    • J. Hyman and M. Shashkov, Mimetic discretizations for Maxwell's equations and the equations of magnetic diffusion, Prog. Electromagnetic Res. 32 (2001) 89-121.
    • (2001) Prog. Electromagnetic Res. , vol.32 , pp. 89-121
    • Hyman, J.1    Shashkov, M.2
  • 14
    • 0000536753 scopus 로고    scopus 로고
    • The numerical solution of diffusion problems in strongly heterogeneous non-isotropic materials
    • J. Hyman, M. Shashkov and S. Steinberg, The numerical solution of diffusion problems in strongly heterogeneous non-isotropic materials, J. Comput. Phys. 132 (1997) 130-148.
    • (1997) J. Comput. Phys. , vol.132 , pp. 130-148
    • Hyman, J.1    Shashkov, M.2    Steinberg, S.3
  • 15
    • 22144481628 scopus 로고    scopus 로고
    • Mimetic finite difference method on polygonal meshes for diffusion-type problems
    • Y. Kuznetsov, K. Lipnikov and M. Shashkov, Mimetic finite difference method on polygonal meshes for diffusion-type problems, Comp. Geosci. 8 (2004) 301-324.
    • (2004) Comp. Geosci. , vol.8 , pp. 301-324
    • Kuznetsov, Y.1    Lipnikov, K.2    Shashkov, M.3
  • 16
    • 4544253720 scopus 로고    scopus 로고
    • Mimetic finite difference methods for diffusion equations on non-orthogonal non-conformal meshes
    • K. Lipnikov, J. Morel and M. Shashkov, Mimetic finite difference methods for diffusion equations on non-orthogonal non-conformal meshes, J. Comput. Phys. 199 (2004) 589-597.
    • (2004) J. Comput. Phys. , vol.199 , pp. 589-597
    • Lipnikov, K.1    Morel, J.2    Shashkov, M.3
  • 17
    • 26944473988 scopus 로고    scopus 로고
    • The mimetic finite difference discretization of diffusion problem on unstructured polyhedral meshes
    • K. Lipnikov, M. Shashkov and D. Svyatskiy, The mimetic finite difference discretization of diffusion problem on unstructured polyhedral meshes, J. Comput. Phys. 211 (2005) 473-491.
    • (2005) J. Comput. Phys. , vol.211 , pp. 473-491
    • Lipnikov, K.1    Shashkov, M.2    Svyatskiy, D.3
  • 18
    • 0036927302 scopus 로고    scopus 로고
    • Nonconforming finite volume methods
    • I. Mishev, Nonconforming finite volume methods, Comp. Geosci. 6 (2002) 253-268.
    • (2002) Comp. Geosci. , vol.6 , pp. 253-268
    • Mishev, I.1
  • 19
    • 0012351695 scopus 로고    scopus 로고
    • A local support-operators diffusion discretization scheme for hexahedral meshes
    • J. Morel, M. Hall and M. Shashkov, A local support-operators diffusion discretization scheme for hexahedral meshes, J. Comput. Phys. 170 (2001) 338-372.
    • (2001) J. Comput. Phys. , vol.170 , pp. 338-372
    • Morel, J.1    Hall, M.2    Shashkov, M.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.