메뉴 건너뛰기




Volumn 113, Issue 3, 2009, Pages 325-356

Convergence analysis of the high-order mimetic finite difference method

Author keywords

[No Author keywords available]

Indexed keywords


EID: 71549140062     PISSN: 0029599X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00211-009-0234-6     Document Type: Article
Times cited : (56)

References (30)
  • 2
    • 0036410391 scopus 로고    scopus 로고
    • Unified analysis of discontinuous galerkin methods for elliptic problems
    • Arnold D.N., Brezzi F., Cockburn B., Marini L.D.: Unified analysis of discontinuous galerkin methods for elliptic problems. SIAM J. Numer. Anal. 39(5), 1749-1779 (2002).
    • (2002) SIAM J. Numer. Anal , vol.39 , Issue.5 , pp. 1749-1779
    • Arnold, D.N.1    Brezzi, F.2    Cockburn, B.3    Marini, L.D.4
  • 3
    • 71549162351 scopus 로고    scopus 로고
    • Beirão da Veiga, L.: A mimetic finite difference method for linear elasticity (submitted)
    • Beirão da Veiga, L.: A mimetic finite difference method for linear elasticity (submitted).
  • 4
    • 37449025866 scopus 로고    scopus 로고
    • A residual based error estimator for the mimetic finite difference method
    • Beirão da Veiga L.: A residual based error estimator for the mimetic finite difference method. Numer. Math. 108(3), 387-406 (2008).
    • (2008) Numer. Math , vol.108 , Issue.3 , pp. 387-406
    • da Veiga, L.B.1
  • 5
    • 71549141058 scopus 로고    scopus 로고
    • Beirão da Veiga, L., Lipnikov, K., Manzini, G.: Convergence analysis of the high-order mimetic finite difference method. Technical Report 14PV08/13/0, IMATI-CNR, via Ferrata, 1, 27100 Pavia, Italy (2008)
    • Beirão da Veiga, L., Lipnikov, K., Manzini, G.: Convergence analysis of the high-order mimetic finite difference method. Technical Report 14PV08/13/0, IMATI-CNR, via Ferrata, 1, 27100 Pavia, Italy (2008).
  • 6
    • 60949113471 scopus 로고    scopus 로고
    • An a posteriori error estimator for the mimetic finite difference approximation of elliptic problems
    • Beirão da Veiga L., Manzini G.: An a posteriori error estimator for the mimetic finite difference approximation of elliptic problems. Int. J. Numer. Meth. Eng. 76(11), 1696-1723 (2008).
    • (2008) Int. J. Numer. Meth. Eng , vol.76 , Issue.11 , pp. 1696-1723
    • da Veiga, L.B.1    Manzini, G.2
  • 7
    • 68549140230 scopus 로고    scopus 로고
    • A higher-order formulation of the mimetic finite difference method
    • Beirão da Veiga L., Manzini G.: A higher-order formulation of the mimetic finite difference method. SIAM J. Sci. Comput. 31(1), 732-760 (2008).
    • (2008) SIAM J. Sci. Comput , vol.31 , Issue.1 , pp. 732-760
    • da Veiga, L.B.1    Manzini, G.2
  • 8
    • 0039483051 scopus 로고    scopus 로고
    • Algorithm 817 P2MESH: Generic object-oriented interface between 2-D unstructured meshes and FEM/FVM-based PDE solvers
    • Bertolazzi E., Manzini G.: Algorithm 817 P2MESH: generic object-oriented interface between 2-D unstructured meshes and FEM/FVM-based PDE solvers. ACM Trans. Math. Softw. 28(1), 101-132 (2002).
    • (2002) ACM Trans. Math. Softw , vol.28 , Issue.1 , pp. 101-132
    • Bertolazzi, E.1    Manzini, G.2
  • 10
    • 66249138493 scopus 로고    scopus 로고
    • Mimetic finite differences for elliptic problems
    • Brezzi F., Buffa A., Lipnikov K.: Mimetic finite differences for elliptic problems. Math. Mod. Numer. Anal. 43, 277-295 (2009).
    • (2009) Math. Mod. Numer. Anal , vol.43 , pp. 277-295
    • Brezzi, F.1    Buffa, A.2    Lipnikov, K.3
  • 11
    • 26944484259 scopus 로고    scopus 로고
    • Convergence of the mimetic finite difference method for diffusion problems on polyhedral meshes
    • Brezzi F., Lipnikov K., Shashkov M.: Convergence of the mimetic finite difference method for diffusion problems on polyhedral meshes. SIAM J. Numer. Anal. 43(5), 1872-1896 (2005).
    • (2005) SIAM J. Numer. Anal , vol.43 , Issue.5 , pp. 1872-1896
    • Brezzi, F.1    Lipnikov, K.2    Shashkov, M.3
  • 12
    • 32644433326 scopus 로고    scopus 로고
    • Convergence of mimetic finite difference method for diffusion problems on polyhedral meshes with curved faces
    • Brezzi F., Lipnikov K., Shashkov M.: Convergence of mimetic finite difference method for diffusion problems on polyhedral meshes with curved faces. Math. Models Methods Appl. Sci. 16(2), 275-297 (2006).
    • (2006) Math. Models Methods Appl. Sci , vol.16 , Issue.2 , pp. 275-297
    • Brezzi, F.1    Lipnikov, K.2    Shashkov, M.3
  • 13
    • 34447101360 scopus 로고    scopus 로고
    • A new discretization methodology for diffusion problems on generalized polyhedral meshes
    • Brezzi F., Lipnikov K., Shashkov M., Simoncini V.: A new discretization methodology for diffusion problems on generalized polyhedral meshes. Comput. Methods Appl. Mech. Eng. 196, 3682-3692 (2007).
    • (2007) Comput. Methods Appl. Mech. Eng , vol.196 , pp. 3682-3692
    • Brezzi, F.1    Lipnikov, K.2    Shashkov, M.3    Simoncini, V.4
  • 14
    • 25144443045 scopus 로고    scopus 로고
    • A family of mimetic finite difference methods on polygonal and polyhedral meshes
    • Brezzi F., Lipnikov K., Simoncini V.: A family of mimetic finite difference methods on polygonal and polyhedral meshes. Math. Models Methods Appl. Sci. 15(10), 1533-1551 (2005).
    • (2005) Math. Models Methods Appl. Sci , vol.15 , Issue.10 , pp. 1533-1551
    • Brezzi, F.1    Lipnikov, K.2    Simoncini, V.3
  • 15
    • 0035922232 scopus 로고    scopus 로고
    • A tensor artificial viscosity using a mimetic finite difference algorithm
    • Campbell J., Shashkov M.: A tensor artificial viscosity using a mimetic finite difference algorithm. J. Comput. Phys. 172, 739-765 (2001).
    • (2001) J. Comput. Phys , vol.172 , pp. 739-765
    • Campbell, J.1    Shashkov, M.2
  • 16
    • 36949012302 scopus 로고    scopus 로고
    • Flux reconstruction and pressure post-processing in mimetic finite difference methods
    • Cangiani A., Manzini G.: Flux reconstruction and pressure post-processing in mimetic finite difference methods. Comput. Methods Appl. Mech. Eng. 197(9-12), 933-945 (2008).
    • (2008) Comput. Methods Appl. Mech. Eng , vol.197 , Issue.9-12 , pp. 933-945
    • Cangiani, A.1    Manzini, G.2
  • 17
    • 1342326610 scopus 로고    scopus 로고
    • A matrix analysis approach to higher-order approximations for divergence and gradients satisfying a global conservation law
    • Castillo J.E., Grone R.D.: A matrix analysis approach to higher-order approximations for divergence and gradients satisfying a global conservation law. SIAM J. Matrix Anal. Appl. 25(1), 128-142 (2003).
    • (2003) SIAM J. Matrix Anal. Appl , vol.25 , Issue.1 , pp. 128-142
    • Castillo, J.E.1    Grone, R.D.2
  • 18
    • 71549152920 scopus 로고    scopus 로고
    • Castillo, J.E., Hyman, J.M., Shashkov, M.J., Steinberg, S.: High-order mimetic finite difference methods on nonuniform grids. In: Ilin, A.V., Scott, L. R. (eds.) Special Issue of Houston Journal of Mathematics, pp. 347-361 (1995)
    • Castillo, J.E., Hyman, J.M., Shashkov, M.J., Steinberg, S.: High-order mimetic finite difference methods on nonuniform grids. In: Ilin, A.V., Scott, L. R. (eds.) Special Issue of Houston Journal of Mathematics, pp. 347-361 (1995).
  • 19
    • 34547521859 scopus 로고    scopus 로고
    • Constitutive equations for discrete electromagnetic problems over polyhedral grids
    • Codecasa L., Trevisan F.: Constitutive equations for discrete electromagnetic problems over polyhedral grids. J. Comput. Phys. 225(2), 1894-1918 (2007).
    • (2007) J. Comput. Phys , vol.225 , Issue.2 , pp. 1894-1918
    • Codecasa, L.1    Trevisan, F.2
  • 20
    • 33645771466 scopus 로고    scopus 로고
    • New element lops time off CFD simulations
    • Dvorak P.: New element lops time off CFD simulations. Mashine Des. 78(169), 154-155 (2006).
    • (2006) Mashine Des , vol.78 , Issue.169 , pp. 154-155
    • Dvorak, P.1
  • 21
    • 33947215151 scopus 로고    scopus 로고
    • A new finite volume scheme for anisotropic diffusion problems on general grids: Convergence analysis
    • Eymard R., Gallouët T., Herbin R.: A new finite volume scheme for anisotropic diffusion problems on general grids: convergence analysis. C. R. Math. Acad. Sci. Paris 344(6), 403-406 (2007).
    • (2007) C. R. Math. Acad. Sci. Paris , vol.344 , Issue.6 , pp. 403-406
    • Eymard, R.1    Gallouët, T.2    Herbin, R.3
  • 22
    • 50249099733 scopus 로고    scopus 로고
    • High-order mimetic finite difference method for diffusion problems on polygonal meshes
    • Gyrya V., Lipnikov K.: High-order mimetic finite difference method for diffusion problems on polygonal meshes. J. Comput. Phys. 227(20), 8841-8854 (2008).
    • (2008) J. Comput. Phys , vol.227 , Issue.20 , pp. 8841-8854
    • Gyrya, V.1    Lipnikov, K.2
  • 23
    • 0001072763 scopus 로고    scopus 로고
    • A finite volume method for the approximation of diffusion operators on distorted meshes
    • Hermeline F.: A finite volume method for the approximation of diffusion operators on distorted meshes. J. Comput. Phys. 160(2), 481-499 (2000).
    • (2000) J. Comput. Phys , vol.160 , Issue.2 , pp. 481-499
    • Hermeline, F.1
  • 24
    • 84875677944 scopus 로고    scopus 로고
    • Mimetic discretizations for Maxwell's equations and the equations of magnetic diffusion
    • Hyman J., Shashkov M.: Mimetic discretizations for Maxwell's equations and the equations of magnetic diffusion. Progress Electromagn. Res. 32, 89-121 (2001).
    • (2001) Progress Electromagn. Res , vol.32 , pp. 89-121
    • Hyman, J.1    Shashkov, M.2
  • 25
    • 0000536753 scopus 로고    scopus 로고
    • The numerical solution of diffusion problems in strongly heterogeneous non-isotropic materials
    • Hyman J., Shashkov M., Steinberg S.: The numerical solution of diffusion problems in strongly heterogeneous non-isotropic materials. J. Comput. Phys. 132, 130-148 (1997).
    • (1997) J. Comput. Phys , vol.132 , pp. 130-148
    • Hyman, J.1    Shashkov, M.2    Steinberg, S.3
  • 26
    • 0038136552 scopus 로고    scopus 로고
    • New mixed finite element method on polygonal and polyhedral meshes
    • Kuznetsov Y., Repin S.: New mixed finite element method on polygonal and polyhedral meshes. Russ. J. Numer. Anal. Math. Modelling 18(3), 261-278 (2003).
    • (2003) Russ. J. Numer. Anal. Math. Modelling , vol.18 , Issue.3 , pp. 261-278
    • Kuznetsov, Y.1    Repin, S.2
  • 29
    • 0001965060 scopus 로고    scopus 로고
    • A local support-operators diffusion discretization scheme for quadrilateral r-z meshes
    • Morel J., Roberts R., Shashkov M.: A local support-operators diffusion discretization scheme for quadrilateral r-z meshes. J. Comput. Phys. 144, 17-51 (1998).
    • (1998) J. Comput. Phys , vol.144 , pp. 17-51
    • Morel, J.1    Roberts, R.2    Shashkov, M.3
  • 30
    • 33750299447 scopus 로고    scopus 로고
    • Higher-order mimetic methods for unstructured meshes
    • Perot J.B., Subramanian V.: Higher-order mimetic methods for unstructured meshes. J. Comput. Phys. 219(1), 68-85 (2006).
    • (2006) J. Comput. Phys , vol.219 , Issue.1 , pp. 68-85
    • Perot, J.B.1    Subramanian, V.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.