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Volumn 8, Issue 4, 2004, Pages 301-324

The mimetic finite difference method on polygonal meshes for diffusion-type problems

Author keywords

Diffusion equation; Locally conservative method; Mimetic discretization

Indexed keywords

DARCY LAW; FINITE DIFFERENCE METHOD; FLOW MODELING;

EID: 22144481628     PISSN: 14200597     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10596-004-3771-1     Document Type: Article
Times cited : (87)

References (23)
  • 1
    • 0001476939 scopus 로고    scopus 로고
    • Mixed finite element methods on non-matching multiblock grids
    • 10.1137/S0036142996308447
    • T. Arbogast, L. Cowsar, M. Wheeler and I. Yotov, Mixed finite element methods on non-matching multiblock grids, SIAM J. Numer. Anal. 37 (2000) 1295-1315. 10.1137/S0036142996308447
    • (2000) SIAM J. Numer. Anal. , vol.37 , pp. 1295-1315
    • Arbogast, T.1    Cowsar, L.2    Wheeler, M.3    Yotov, I.4
  • 2
    • 0035708126 scopus 로고    scopus 로고
    • Convergence of mimetic finite difference discretizations of the diffusion equation
    • M. Berndt, K. Lipnikov, D. Moulton and M. Shashkov, Convergence of mimetic finite difference discretizations of the diffusion equation, J. Numer. Math. 9 (2001) 265-284.
    • (2001) J. Numer. Math. , vol.9 , pp. 265-284
    • Berndt, M.1    Lipnikov, K.2    Moulton, D.3    Shashkov, M.4
  • 3
    • 22144455832 scopus 로고    scopus 로고
    • Superconvergence of the velocity in mimetic finite difference methods on quadrilaterals
    • Los Alamos Report LA-UR-03-7904 (submitted to SIAM J. Numer. Anal.)
    • M. Berndt, K. Lipnikov, M. Shashkov, M. Wheeler and I. Yotov, Superconvergence of the velocity in mimetic finite difference methods on quadrilaterals, Los Alamos Report LA-UR-03-7904 (submitted to SIAM J. Numer. Anal.).
    • Berndt, M.1    Lipnikov, K.2    Shashkov, M.3    Wheeler, M.4    Yotov, I.5
  • 4
    • 0035922232 scopus 로고    scopus 로고
    • A tensor artificial viscosity using a mimetic finite difference algorithm
    • 10.1006/jcph.2001.6856
    • J. Campbell and M. Shashkov, A tensor artificial viscosity using a mimetic finite difference algorithm, J. Comput. Phys. 172 (2001) 739-765. 10.1006/jcph.2001.6856
    • (2001) J. Comput. Phys. , vol.172 , pp. 739-765
    • Campbell, J.1    Shashkov, M.2
  • 5
    • 84966249747 scopus 로고
    • Local refinement techniques for elliptic problems on cell-centered grids I, error analysis
    • R.E. Ewing, R.D. Lazarov and P.S. Vassilevski, Local refinement techniques for elliptic problems on cell-centered grids I, error analysis, Math. Comp. 56 (1991) 437-461.
    • (1991) Math. Comp. , vol.56 , pp. 437-461
    • Ewing, R.E.1    Lazarov, R.D.2    Vassilevski, P.S.3
  • 6
    • 0001367937 scopus 로고    scopus 로고
    • Superconvergence of mixed finite element approximations over quadrilaterals
    • 10.1137/S0036142997322801
    • R.E. Ewing, M. Liu and J. Wang, Superconvergence of mixed finite element approximations over quadrilaterals, SIAM J. Numer. Anal. 36(3) (1999) 772-787. 10.1137/S0036142997322801
    • (1999) SIAM J. Numer. Anal. , vol.36 , Issue.3 , pp. 772-787
    • Ewing, R.E.1    Liu, M.2    Wang, J.3
  • 7
    • 0036923031 scopus 로고    scopus 로고
    • Mimetic finite difference methods for diffusion equations
    • 10.1023/A:1021282912658
    • J. Hyman, J. Morel, M. Shashkov and S. Steinberg, Mimetic finite difference methods for diffusion equations, Comput. Geosci. 6(3/4) (2002) 333-352. 10.1023/A:1021282912658
    • (2002) Comput. Geosci. , vol.6 , Issue.3-4 , pp. 333-352
    • Hyman, J.1    Morel, J.2    Shashkov, M.3    Steinberg, S.4
  • 8
    • 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, Progress Electromagnetic Res. 32 (2001) 89-121.
    • (2001) Progress Electromagnetic Res. , vol.32 , pp. 89-121
    • Hyman, J.1    Shashkov, M.2
  • 9
    • 0000536753 scopus 로고    scopus 로고
    • The numerical solution of diffusion problems in strongly heterogeneous non-isotropic materials
    • 10.1006/jcph.1996.5633
    • 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. 10.1006/jcph.1996.5633
    • (1997) J. Comput. Phys. , vol.132 , pp. 130-148
    • Hyman, J.1    Shashkov, M.2    Steinberg, S.3
  • 10
    • 0035577026 scopus 로고    scopus 로고
    • The effect of inner products for discrete vector fields on the accuracy of mimetic finite difference methods
    • 10.1016/S0898-1221(01)00260-7
    • J. Hyman, M. Shashkov and S. Steinberg, The effect of inner products for discrete vector fields on the accuracy of mimetic finite difference methods, Internat. J. Comput. Math. Appl. 42 (2001) 1527-1547. 10.1016/ S0898-1221(01)00260-7
    • (2001) Internat. J. Comput. Math. Appl. , vol.42 , pp. 1527-1547
    • Hyman, J.1    Shashkov, M.2    Steinberg, S.3
  • 11
    • 22144460821 scopus 로고    scopus 로고
    • Two-level preconditioners with projectors for unstructured grids
    • Y. Kuznetsov, Two-level preconditioners with projectors for unstructured grids, Russian J. Numer. Anal. Math. Modelling 15(3/4) (2000) 247-256.
    • (2000) Russian J. Numer. Anal. Math. Modelling , vol.15 , Issue.3-4 , pp. 247-256
    • Kuznetsov, Y.1
  • 12
    • 0038136552 scopus 로고    scopus 로고
    • New mixed finite element method on polygonal and polyhedral meshes
    • 10.1163/156939803322380846
    • Y. Kuznetsov and S. Repin, New mixed finite element method on polygonal and polyhedral meshes, Russian J. Numer. Anal. Math. Modelling 18(3) (2003) 261-278. 10.1163/156939803322380846
    • (2003) Russian J. Numer. Anal. Math. Modelling , vol.18 , Issue.3 , pp. 261-278
    • Kuznetsov, Y.1    Repin, S.2
  • 13
    • 4544253720 scopus 로고    scopus 로고
    • Mimetic finite difference methods for diffusion equations on non-orthogonal non-conformal meshes
    • 10.1016/j.jcp.2004.02.016
    • 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. 10.1016/j.jcp.2004.02.016
    • (2004) J. Comput. Phys. , vol.199 , pp. 589-597
    • Lipnikov, K.1    Morel, J.2    Shashkov, M.3
  • 14
    • 4344619323 scopus 로고    scopus 로고
    • Analysis and optimization of inner products for mimetic finite difference method on triangular grid
    • 10.1016/j.matcom.2004.05.008
    • R. Liska, M. Shashkov and V. Ganzha, Analysis and optimization of inner products for mimetic finite difference method on triangular grid, Math. Comput. Simulation 67 (2004) 55-66. 10.1016/j.matcom.2004.05.008
    • (2004) Math. Comput. Simulation , vol.67 , pp. 55-66
    • Liska, R.1    Shashkov, M.2    Ganzha, V.3
  • 15
    • 0034235159 scopus 로고    scopus 로고
    • A discrete operator calculus for finite difference approximations
    • 10.1016/S0045-7825(00)80001-8
    • L. Margolin, M. Shashkov and P. Smolarkiewicz, A discrete operator calculus for finite difference approximations, Comput. Methods Appl. Mech. Engrg. 187 (2000) 365-383. 10.1016/S0045-7825(00)80001-8
    • (2000) Comput. Methods Appl. Mech. Engrg. , vol.187 , pp. 365-383
    • Margolin, L.1    Shashkov, M.2    Smolarkiewicz, P.3
  • 16
    • 0001965060 scopus 로고    scopus 로고
    • A local support-operators diffusion discretization scheme for quadrilateral r - Z meshes
    • 10.1006/jcph.1998.5981
    • J. Morel, R. Roberts and M. Shashkov, A local support-operators diffusion discretization scheme for quadrilateral r - z meshes, J. Comput. Phys. 144 (1998) 17-51. 10.1006/jcph.1998.5981
    • (1998) J. Comput. Phys. , vol.144 , pp. 17-51
    • Morel, J.1    Roberts, R.2    Shashkov, M.3
  • 17
    • 0036929306 scopus 로고    scopus 로고
    • Shape functions for velocity interpolation in general hexahedral cells
    • 10.1023/A:1021218525861
    • R. Naff, T. Russell and J. Wilson, Shape functions for velocity interpolation in general hexahedral cells, Comput. Geosci. 6(3/4) (2002) 285-314. 10.1023/A:1021218525861
    • (2002) Comput. Geosci. , vol.6 , Issue.3-4 , pp. 285-314
    • Naff, R.1    Russell, T.2    Wilson, J.3
  • 19
    • 0035546588 scopus 로고    scopus 로고
    • Discretizing the diffusion equation on unstructured polygonal meshes in two dimensions
    • 10.1016/S0306-4549(01)00007-X
    • T.S. Palmer, Discretizing the diffusion equation on unstructured polygonal meshes in two dimensions, Ann. Nuclear Energy 28 (2001) 1851-1880. 10.1016/S0306-4549(01)00007-X
    • (2001) Ann. Nuclear Energy , vol.28 , pp. 1851-1880
    • Palmer, T.S.1
  • 21
    • 0030525010 scopus 로고    scopus 로고
    • Solving diffusion equations with rough coefficients in rough grids
    • 10.1006/jcph.1996.0257
    • M. Shashkov and S. Steinberg, Solving diffusion equations with rough coefficients in rough grids, J. Comput. Phys. 129 (1996) 383-405. 10.1006/jcph.1996.0257
    • (1996) J. Comput. Phys. , vol.129 , pp. 383-405
    • Shashkov, M.1    Steinberg, S.2
  • 22
    • 0002621183 scopus 로고
    • Algebraic multigrid (AMG): Experiences and comparisons
    • 10.1016/0096-3003(83)90023-1
    • K. Stüben, Algebraic multigrid (AMG): Experiences and comparisons, Appl. Math. Comput. 13 (1983) 419-452. 10.1016/0096-3003(83)90023-1
    • (1983) Appl. Math. Comput. , vol.13 , pp. 419-452
    • Stüben, K.1
  • 23
    • 0041034172 scopus 로고    scopus 로고
    • Convergence of algebraic multigrid based on smoothed aggregation
    • 10.1007/s211-001-8015-y
    • P. Van̂k, M. Brezina and J. Mandel, Convergence of algebraic multigrid based on smoothed aggregation, Numer. Math. 88 (2001) 559-579. 10.1007/s211-001-8015-y
    • (2001) Numer. Math. , vol.88 , pp. 559-579
    • Van̂k, P.1    Brezina, M.2    Mandel, J.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.