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Volumn 14, Issue 2, 1998, Pages 193-212

Finite Volume Methods on Voronoi Meshes

Author keywords

Cell centered finite differences; Error estimates; Upwind approximations

Indexed keywords


EID: 0000774381     PISSN: 0749159X     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1098-2426(199803)14:2<193::AID-NUM4>3.0.CO;2-J     Document Type: Article
Times cited : (117)

References (41)
  • 1
    • 0001392592 scopus 로고
    • Differencing of the diffusion equation in lagrangian hydrodynamic codes
    • D. S. Kershaw, "Differencing of the diffusion equation in lagrangian hydrodynamic codes," J. Comput. Phys. 39, 375-395 (1987).
    • (1987) J. Comput. Phys. , vol.39 , pp. 375-395
    • Kershaw, D.S.1
  • 2
    • 0000898457 scopus 로고
    • Homogeneous difference schemes on nonuniform nets
    • Russian
    • A. N. Tikhonov and A. A. Samarskii, "Homogeneous difference schemes on nonuniform nets," Zh. Vychisl. Mat. i Mat. Fiz 2, 812-832 (1962) (Russian).
    • (1962) Zh. Vychisl. Mat. i Mat. Fiz , vol.2 , pp. 812-832
    • Tikhonov, A.N.1    Samarskii, A.A.2
  • 4
    • 84966240649 scopus 로고
    • The numerical solution of second order boundary value problems on nonuniform meshes
    • T. A. Manteuffel and A. B. White, Jr., "The numerical solution of second order boundary value problems on nonuniform meshes," Math. Comp. 47, 511-535 (1986).
    • (1986) Math. Comp. , vol.47 , pp. 511-535
    • Manteuffel, T.A.1    White Jr., A.B.2
  • 6
    • 0040010532 scopus 로고
    • Analysis of finite volume methods
    • Universite de Pau et des Pays de L'adour, Pau, France
    • J. M. Thomas and D. Trujillo, "Analysis of finite volume methods," Technical Report 19, Universite de Pau et des Pays de L'adour, Pau, France, 1995.
    • (1995) Technical Report 19
    • Thomas, J.M.1    Trujillo, D.2
  • 7
    • 0041197869 scopus 로고
    • Convergence of finite volume methods
    • Universite de Pau et des Pays de L'adour, Pau, France
    • J. M. Thomas and D. Trujillo, "Convergence of finite volume methods," Technical Report 20, Universite de Pau et des Pays de L'adour, Pau, France, 1995.
    • (1995) Technical Report 20
    • Thomas, J.M.1    Trujillo, D.2
  • 8
    • 0001198473 scopus 로고    scopus 로고
    • Mixed finite elements for elliptic problems with tensor coefficients as cell-centered finite differences
    • T. Arbogast, M. F. Wheeler, and I. Yotov, "Mixed finite elements for elliptic problems with tensor coefficients as cell-centered finite differences," SIAM J. Numer. Anal. 34, 828-353 (1997).
    • (1997) SIAM J. Numer. Anal. , vol.34 , pp. 828-1353
    • Arbogast, T.1    Wheeler, M.F.2    Yotov, I.3
  • 9
    • 0001669414 scopus 로고
    • On convergence of block-centered finite differences for elliptic problems
    • A. Weiser and M. F. Wheeler, "On convergence of block-centered finite differences for elliptic problems," SIAM J. Numer. Anal. 25, 351-375 (1988).
    • (1988) SIAM J. Numer. Anal. , vol.25 , pp. 351-375
    • Weiser, A.1    Wheeler, M.F.2
  • 12
    • 0001063435 scopus 로고
    • On the finite volume element method
    • Z. Cai, "On the finite volume element method," Numer. Math. 58, 713-735 (1991).
    • (1991) Numer. Math. , vol.58 , pp. 713-735
    • Cai, Z.1
  • 13
    • 34250073797 scopus 로고
    • Box schemes on quadrilateral meshes
    • T. Schmidt, "Box schemes on quadrilateral meshes," Computing 51, 271-292 (1993).
    • (1993) Computing , vol.51 , pp. 271-292
    • Schmidt, T.1
  • 14
    • 0001416923 scopus 로고
    • Finite difference schemes on triangular cell-centered grids with local refinement
    • P. S. Vassilevski, S. I. Petrova, and R. D. Lazarov, "Finite difference schemes on triangular cell-centered grids with local refinement," SIAM J. Sci. Stat. Comput. 13, 1287-1313 (1992).
    • (1992) SIAM J. Sci. Stat. Comput. , vol.13 , pp. 1287-1313
    • Vassilevski, P.S.1    Petrova, S.I.2    Lazarov, R.D.3
  • 15
    • 84985371470 scopus 로고
    • An error estimate for a finite volume scheme for a diffusion-convection problem on a triangular mesh
    • R. Herbin, "An error estimate for a finite volume scheme for a diffusion-convection problem on a triangular mesh," Numer. Meth. for Partial Diff. Equat. 11, 165-174 (1995).
    • (1995) Numer. Meth. for Partial Diff. Equat. , vol.11 , pp. 165-174
    • Herbin, R.1
  • 17
    • 0000561839 scopus 로고
    • Finite volume methods and their analysis
    • K. W. Morton and E. Süli, "Finite volume methods and their analysis," IMA J. Numer. Anal. 11, 241-260 (1991).
    • (1991) IMA J. Numer. Anal. , vol.11 , pp. 241-260
    • Morton, K.W.1    Süli, E.2
  • 18
    • 84968518361 scopus 로고
    • Finite volume solutions of convection-diffusion test problems
    • J. A. Mackenzie and K. W. Morton. Finite volume solutions of convection-diffusion test problems. Math. Comp. 60, 189-220, 1992.
    • (1992) Math. Comp. , vol.60 , pp. 189-220
    • Mackenzie, J.A.1    Morton, K.W.2
  • 19
    • 84968482080 scopus 로고
    • The accuracy of cell vertex finite volume methods on quadrilateral meshes
    • E. Süli, "The accuracy of cell vertex finite volume methods on quadrilateral meshes," Math. Comp. 59, 359-382 (1992).
    • (1992) Math. Comp. , vol.59 , pp. 359-382
    • Süli, E.1
  • 23
    • 0001218055 scopus 로고
    • ∞ stability of finite element approximations of elliptic gradient equations
    • ∞ stability of finite element approximations of elliptic gradient equations," Numer. Math. 57, 561-575 (1990).
    • (1990) Numer. Math. , vol.57 , pp. 561-575
    • Kerhoven, T.1    Jerome, J.W.2
  • 25
    • 0028372347 scopus 로고
    • Modeling vertical and horizontal wells with voronoi grids
    • C. L. Palagi and K. Aziz, "Modeling vertical and horizontal wells with voronoi grids," SPE Reservoir Engineering, February, 15-21 (1994).
    • (1994) SPE Reservoir Engineering , vol.FEBRUARY , pp. 15-21
    • Palagi, C.L.1    Aziz, K.2
  • 26
    • 0007718564 scopus 로고
    • An introduction to finite volume methods for linear elliptic equations of second order
    • Friedrich-Alexander University of Erlangen-Nuremberg, Erlangen
    • L. Angermann, "An introduction to finite volume methods for linear elliptic equations of second order," Technical Report No. 163, Friedrich-Alexander University of Erlangen-Nuremberg, Erlangen, 1995.
    • (1995) Technical Report No. 163
    • Angermann, L.1
  • 27
  • 29
    • 0030395317 scopus 로고    scopus 로고
    • Relations between FEM and FVM applied to the Poisson equation
    • R. Vanselow, "Relations between FEM and FVM applied to the Poisson equation," Computing 57, 93-104 (1996).
    • (1996) Computing , vol.57 , pp. 93-104
    • Vanselow, R.1
  • 30
    • 84976826673 scopus 로고
    • Voronoi diagrams - A survey of a fundamental geometric data structure
    • F. Aurenhammer, "Voronoi diagrams - A survey of a fundamental geometric data structure," ACM Comput. Surveys, 23, 345-405 (1991).
    • (1991) ACM Comput. Surveys , vol.23 , pp. 345-405
    • Aurenhammer, F.1
  • 31
    • 0001465710 scopus 로고
    • Voronoi diagrams and Delaunay triangulations
    • Computing in Euclidean Geometry, D. Z. Du and F. K. Hwang, editors, World Scientific
    • S. Fortune, "Voronoi diagrams and Delaunay triangulations," in Computing in Euclidean Geometry, Volume 1 of Lecture Notes Series of Computing, D. Z. Du and F. K. Hwang, editors, World Scientific, 1992, pp. 193-233.
    • (1992) Lecture Notes Series of Computing , vol.1 , pp. 193-233
    • Fortune, S.1
  • 33
    • 0001914423 scopus 로고
    • Mesh generation and optimal triangulation
    • Computing in Euclidean Geometry, D. Z. Du and F. K. Hwang, Eds., World Scientific
    • M. Bern and D. Eppstein, "Mesh generation and optimal triangulation," in Computing in Euclidean Geometry, volume 1 of Lecture Notes Series of Computing, D. Z. Du and F. K. Hwang, Eds., World Scientific, 1992, pp. 23-90.
    • (1992) Lecture Notes Series of Computing , vol.1 , pp. 23-90
    • Bern, M.1    Eppstein, D.2
  • 36
    • 0001782272 scopus 로고
    • On a conservative upwind finite element scheme for convection diffusion equations
    • K. Baba and M. Tabata, "On a conservative upwind finite element scheme for convection diffusion equations," R.A.I.R.O. Analyse numerique/Numerical Anal. 15, 3-25 (1981).
    • (1981) R.A.I.R.O. Analyse Numerique/Numerical Anal. , vol.15 , pp. 3-25
    • Baba, K.1    Tabata, M.2
  • 37
  • 40
    • 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, 437-461 (1991).
    • (1991) Math. Comp. , vol.56 , pp. 437-461
    • Ewing, R.E.1    Lazarov, R.D.2    Vassilevski, P.S.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.