메뉴 건너뛰기




Volumn 33, Issue 4, 1997, Pages 81-104

Natural discretizations for the divergence, gradient, and curl on logically rectangular grids

Author keywords

Discrete vector analysis; Finite difference; Logically rectangular grids

Indexed keywords

CURVE FITTING; FUNCTIONS; INTEGRAL EQUATIONS; MATHEMATICAL OPERATORS; THEOREM PROVING; VECTORS;

EID: 0031071242     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0898-1221(97)00009-6     Document Type: Article
Times cited : (177)

References (66)
  • 2
    • 0040006469 scopus 로고
    • Employment of the reference-operator method in the construction of finite difference analogs of tensor operations
    • A.A. Samarskii, V.F. Tishkin, A.P. Favorskii and M.Yu. Shashkov, Employment of the reference-operator method in the construction of finite difference analogs of tensor operations, Diff. Eqns. 18, 881-885, (1982).
    • (1982) Diff. Eqns. , vol.18 , pp. 881-885
    • Samarskii, A.A.1    Tishkin, V.F.2    Favorskii, A.P.3    Shashkov, M.Yu.4
  • 4
    • 0040599659 scopus 로고
    • The convergence of difference schemes for two-dimensional equations of acoustics and Maxwell's equations
    • N.V. Ardelyan, The convergence of difference schemes for two-dimensional equations of acoustics and Maxwell's equations, USSR Comput. Math. and Math. Phys. 23 (5), 93-99, (1983).
    • (1983) USSR Comput. Math. and Math. Phys. , vol.23 , Issue.5 , pp. 93-99
    • Ardelyan, N.V.1
  • 5
    • 0041193705 scopus 로고
    • Convergence of difference schemes for two-dimensional gas-dynamic equations in acoustics approximations with gravitation taken into account
    • Translated from Russian by Consultants Bureau Corp.
    • N.V. Ardelyan and S.V. Chernigovskii, Convergence of difference schemes for two-dimensional gas-dynamic equations in acoustics approximations with gravitation taken into account, Translated from Russian by Consultants Bureau Corp., Diff. Eqns. 20 (7), 807-813, (1984).
    • (1984) Diff. Eqns. , vol.20 , Issue.7 , pp. 807-813
    • Ardelyan, N.V.1    Chernigovskii, S.V.2
  • 6
    • 0041193706 scopus 로고
    • Method of investigating the convergence of nonlinear finite-difference schemes
    • N.V. Ardelyan, Method of investigating the convergence of nonlinear finite-difference schemes, Diff. Eqns. 23 (7), 737-745, (1987).
    • (1987) Diff. Eqns. , vol.23 , Issue.7 , pp. 737-745
    • Ardelyan, N.V.1
  • 7
    • 38249021342 scopus 로고
    • The convergence to generalized solutions of difference schemes of the reference-operator method for Poisson's equation
    • A.A. Denisov, A.V. Koldoba and Yu.A. Poveshchenko, The convergence to generalized solutions of difference schemes of the reference-operator method for Poisson's equation, USSR Comput. Math. and Math. Phys. 29 (2), 32-38, (1989).
    • (1989) USSR Comput. Math. and Math. Phys. , vol.29 , Issue.2 , pp. 32-38
    • Denisov, A.A.1    Koldoba, A.V.2    Poveshchenko, Yu.A.3
  • 8
    • 0041193704 scopus 로고
    • The approximation of differential operators on nonorthogonal meshes
    • A.V. Koldoba, Yu.A. Poveshchenko and Yu.P. Popov, The approximation of differential operators on nonorthogonal meshes, Diff. Eqns. 19 (7), 919-927, (1983).
    • (1983) Diff. Eqns. , vol.19 , Issue.7 , pp. 919-927
    • Koldoba, A.V.1    Poveshchenko, Yu.A.2    Popov, Yu.P.3
  • 9
    • 0008463183 scopus 로고
    • Difference schemes for the Navier-Stokes equations on a net consisting of Dirichlet cells, english translation of Zhurnal vychislitel'noi matematiki i matematicheskoi fiziki
    • Yu.V. Apanovich and E.D. Lymkis, Difference schemes for the Navier-Stokes equations on a net consisting of Dirichlet cells, English translation of Zhurnal vychislitel'noi matematiki i matematicheskoi fiziki., USSR Comput. Math. and Math. Phys. 28 (2), 57-63, (1988).
    • (1988) USSR Comput. Math. and Math. Phys. , vol.28 , Issue.2 , pp. 57-63
    • Apanovich, Yu.V.1    Lymkis, E.D.2
  • 11
    • 0040599653 scopus 로고
    • Stability of variational-difference schemes for the problems of gas-dynamics with heat conduction
    • A. Sabitova and E.A. Samarskaya, Stability of variational-difference schemes for the problems of gas-dynamics with heat conduction, Diff. Eqns. 21 (7), 861-864, (1985).
    • (1985) Diff. Eqns. , vol.21 , Issue.7 , pp. 861-864
    • Sabitova, A.1    Samarskaya, E.A.2
  • 12
    • 0041193703 scopus 로고
    • Difference scheme for the "Dirichlet particles" method in cylindrical coordinates, conserving symmetry of gas-dynamical flow
    • A. Solov'ev and M. Shashkov, Difference scheme for the "Dirichlet particles" method in cylindrical coordinates, conserving symmetry of gas-dynamical flow, Diff. Eqns. 24 (7), 817-823, (1988).
    • (1988) Diff. Eqns. , vol.24 , Issue.7 , pp. 817-823
    • Solov'ev, A.1    Shashkov, M.2
  • 15
    • 0039414280 scopus 로고
    • Variational-difference schemes for the heat conduction equation on nonregular grids
    • A. Favorskii, V. Tishkin and M. Shashkov, Variational-difference schemes for the heat conduction equation on nonregular grids, Sov. Phys. Dokl. 24, 446-448, (1979).
    • (1979) Sov. Phys. Dokl. , vol.24 , pp. 446-448
    • Favorskii, A.1    Tishkin, V.2    Shashkov, M.3
  • 16
    • 0011654556 scopus 로고
    • Variational approach to the construction of finite-difference schemes for the diffusion equations for magnetic field
    • A. Favorskii, T. Korshiya, M. Shashkov and V. Tishkin, Variational approach to the construction of finite-difference schemes for the diffusion equations for magnetic field, Diff. Eqns. 18 (7), 863-872, (1982).
    • (1982) Diff. Eqns. , vol.18 , Issue.7 , pp. 863-872
    • Favorskii, A.1    Korshiya, T.2    Shashkov, M.3    Tishkin, V.4
  • 17
    • 0011601576 scopus 로고
    • A variational approach to the construction of difference schemes on curvilinear meshes for heat-conduction equation
    • A. Favorskii, T. Korshiya, M. Shashkov and V. Tishkin, A variational approach to the construction of difference schemes on curvilinear meshes for heat-conduction equation, USSR Comput. Math. and Math. Phys. 20, 135-155, (1980).
    • (1980) USSR Comput. Math. and Math. Phys. , vol.20 , pp. 135-155
    • Favorskii, A.1    Korshiya, T.2    Shashkov, M.3    Tishkin, V.4
  • 18
    • 0001367435 scopus 로고
    • Support-operator finite-difference algorithms for general elliptic problems
    • M. Shashkov and S. Steinberg, Support-operator finite-difference algorithms for general elliptic problems, J. of Comput. Phys. 118, 131-151, (1995).
    • (1995) J. of Comput. Phys. , vol.118 , pp. 131-151
    • Shashkov, M.1    Steinberg, S.2
  • 21
    • 0040006465 scopus 로고
    • The method of step-by-step inversion for numerical solution of the biharmonic equation
    • S.B. Sorokin, The method of step-by-step inversion for numerical solution of the biharmonic equation, Siberian Mathematical Journal 36 (3), 569-573, (1995).
    • (1995) Siberian Mathematical Journal , vol.36 , Issue.3 , pp. 569-573
    • Sorokin, S.B.1
  • 22
    • 0040006461 scopus 로고
    • Numerical methods for static problems of elasticity
    • Translated from Russian by Consultants Bureau, New York, Plenum Publishing Corp.
    • A.N. Konovalov, Numerical methods for static problems of elasticity, Translated from Russian by Consultants Bureau, New York, Plenum Publishing Corp., Siberian Mathematical Journal 36 (3), 491-505, (1995).
    • (1995) Siberian Mathematical Journal , vol.36 , Issue.3 , pp. 491-505
    • Konovalov, A.N.1
  • 23
    • 0040006468 scopus 로고
    • Variational-difference schemes for the dynamical equations for deformable media
    • V.F. Tishkin, Variational-difference schemes for the dynamical equations for deformable media, Diff. Eqns. 21 (7), 865-870, (1985).
    • (1985) Diff. Eqns. , vol.21 , Issue.7 , pp. 865-870
    • Tishkin, V.F.1
  • 25
    • 0040599656 scopus 로고
    • Axisymmetric difference operators in an orthogonal coordinate system
    • V.A. Korobitsin, Axisymmetric difference operators in an orthogonal coordinate system, USSR Comput. Math. and Math. Phys. 29 (6), 13-21, (1989).
    • (1989) USSR Comput. Math. and Math. Phys. , vol.29 , Issue.6 , pp. 13-21
    • Korobitsin, V.A.1
  • 26
    • 0040006462 scopus 로고
    • Basic operators method for construction of difference schemes in curvilinear orthogonal coordinate system
    • V.A. Korobitsin, Basic operators method for construction of difference schemes in curvilinear orthogonal coordinate system, Mathl. Modelling 2 (6), 110-117, (1990).
    • (1990) Mathl. Modelling , vol.2 , Issue.6 , pp. 110-117
    • Korobitsin, V.A.1
  • 27
    • 0002755419 scopus 로고
    • The sensitivity and accuracy of fourth order finite-difference schemes on nonuniform grids in one dimension
    • J. Castillo, J.M. Hyman, M.J. Shashkov and S. Steinberg, The sensitivity and accuracy of fourth order finite-difference schemes on nonuniform grids in one dimension, Computers Math. Applic. 30 (8), 41-55, (1995).
    • (1995) Computers Math. Applic. , vol.30 , Issue.8 , pp. 41-55
    • Castillo, J.1    Hyman, J.M.2    Shashkov, M.J.3    Steinberg, S.4
  • 28
    • 0040599658 scopus 로고
    • Two-dimensional difference schemes of magneto-hydrodynamics on triangle Lagrange meshes
    • V.M. Goloviznin, V.K. Korshunov and A.A. Samarskii, Two-dimensional difference schemes of magneto-hydrodynamics on triangle Lagrange meshes, USSR Comput. Math. and Math. Phys. 22 (4), 160-178, (1982).
    • (1982) USSR Comput. Math. and Math. Phys. , vol.22 , Issue.4 , pp. 160-178
    • Goloviznin, V.M.1    Korshunov, V.K.2    Samarskii, A.A.3
  • 29
    • 0040006467 scopus 로고
    • Approximation of finite-difference operators on a mesh of Dirichlet cells
    • A. Solov'ev, E. Solov'eva, V. Tishkin, A. Favorskii and M. Shashkov, Approximation of finite-difference operators on a mesh of Dirichlet cells, Diff. Eqns. 22 (7), 863-872, (1986).
    • (1986) Diff. Eqns. , vol.22 , Issue.7 , pp. 863-872
    • Solov'ev, A.1    Solov'eva, E.2    Tishkin, V.3    Favorskii, A.4    Shashkov, M.5
  • 39
    • 38249032358 scopus 로고
    • Calculation of the flows of a viscous incompressible liquid with a free surface on two dimensional Lagrangian nets
    • A.V. Demin, V.A. Korobitsyn, A.I. Mazurenko and A.I. Khe, Calculation of the flows of a viscous incompressible liquid with a free surface on two dimensional Lagrangian nets, USSR Comput. Math. and Math. Phys. 28 (6), 81-87, (1988).
    • (1988) USSR Comput. Math. and Math. Phys. , vol.28 , Issue.6 , pp. 81-87
    • Demin, A.V.1    Korobitsyn, V.A.2    Mazurenko, A.I.3    Khe, A.I.4
  • 41
    • 0041193710 scopus 로고
    • Method of orthogonal expansions
    • A.A. Dezin, Method of orthogonal expansions, Siberian Mathematical Journal 9 (4), 788-797, (1968).
    • (1968) Siberian Mathematical Journal , vol.9 , Issue.4 , pp. 788-797
    • Dezin, A.A.1
  • 42
    • 0039414277 scopus 로고
    • Combination model of euclidean space and difference operators
    • A.A. Dezin, Combination model of euclidean space and difference operators, Siberian Mathematical Journal 16 (4), 536-545, (1975).
    • (1975) Siberian Mathematical Journal , vol.16 , Issue.4 , pp. 536-545
    • Dezin, A.A.1
  • 43
    • 0041193709 scopus 로고
    • Natural differential operators and the separation of variables
    • A.A. Dezin, Natural differential operators and the separation of variables, Diff. Eqns. 9 (1), 18-23, (1973).
    • (1973) Diff. Eqns. , vol.9 , Issue.1 , pp. 18-23
    • Dezin, A.A.1
  • 44
    • 0039414281 scopus 로고
    • Some models related to the euler equations
    • A.A. Dezin, Some models related to the euler equations, Diff. Eqns. 6 (1), 12-20, (1970).
    • (1970) Diff. Eqns. , vol.6 , Issue.1 , pp. 12-20
    • Dezin, A.A.1
  • 45
    • 0041088365 scopus 로고
    • Solution of the first boundary-value problem for the Lame's equation by the application of invariant finite-difference operators
    • N.B. Kozhakhmedov, Solution of the first boundary-value problem for the Lame's equation by the application of invariant finite-difference operators, Diff. Eqns. 6 (5), 694-705, (1970).
    • (1970) Diff. Eqns. , vol.6 , Issue.5 , pp. 694-705
    • Kozhakhmedov, N.B.1
  • 46
    • 0039309072 scopus 로고
    • Difference approximations to differential operators of mathematical physics
    • A.L. Krylov, Difference approximations to differential operators of mathematical physics, Soviet Math. Dokl. 9 (1), 138-142, (1968).
    • (1968) Soviet Math. Dokl. , vol.9 , Issue.1 , pp. 138-142
    • Krylov, A.L.1
  • 47
    • 0039414276 scopus 로고
    • Models with finite number of degrees of freedom for class of problems in mathematical physics, (difference systems with conservation laws)
    • A.L. Krylov, Models with finite number of degrees of freedom for class of problems in mathematical physics, (Difference systems with Conservation Laws), Soviet Phys. Dokl. 7, 18-20, (1962).
    • (1962) Soviet Phys. Dokl. , vol.7 , pp. 18-20
    • Krylov, A.L.1
  • 49
    • 0040599654 scopus 로고
    • Method of orthogonal projections for finite-difference analog of one system of equations
    • V.I. Lebedev, Method of orthogonal projections for finite-difference analog of one system of equations, (in Russian), Reports of USSR Academy of Sciences 113 (6), 1206-1209, (1957).
    • (1957) Reports of USSR Academy of Sciences , vol.113 , Issue.6 , pp. 1206-1209
    • Lebedev, V.I.1
  • 50
    • 0041193708 scopus 로고
    • Difference analogues of orthogonal decompositions, basic differential operators and some boundary problems of mathematical physics - I
    • V.I. Lebedev, Difference analogues of orthogonal decompositions, basic differential operators and some boundary problems of mathematical physics - I, USSR Comput. Math. and Math. Phys. 4 (3), 69-92, (1964).
    • (1964) USSR Comput. Math. and Math. Phys. , vol.4 , Issue.3 , pp. 69-92
    • Lebedev, V.I.1
  • 51
    • 0040006466 scopus 로고
    • Difference analogues of orthogonal decompositions, basic differential operators and some boundary problems of mathematical physics - II
    • V.I. Lebedev, Difference analogues of orthogonal decompositions, basic differential operators and some boundary problems of mathematical physics - II, USSR Comput. Math. and Math. Phys. 4 (4), 36-50, (1964).
    • (1964) USSR Comput. Math. and Math. Phys. , vol.4 , Issue.4 , pp. 36-50
    • Lebedev, V.I.1
  • 52
  • 53
    • 84967491274 scopus 로고
    • The method of orthogonal projection in potential theory
    • H. Weil, The method of orthogonal projection in potential theory, Duke Mathematical Journal 7, 411-444, (1940).
    • (1940) Duke Mathematical Journal , vol.7 , pp. 411-444
    • Weil, H.1
  • 55
    • 84968483581 scopus 로고
    • On the convergence of discrete approximations to the Navier-Stokes equations
    • A.J. Chorin, On the Convergence of Discrete Approximations to the Navier-Stokes Equations, Math. Comput. 23, 341-353, (1969).
    • (1969) Math. Comput. , vol.23 , pp. 341-353
    • Chorin, A.J.1
  • 58
    • 0026822185 scopus 로고
    • Direct discretization of planar DIV-CURL problems
    • R.A. Nicolaides, Direct discretization of planar DIV-CURL problems, SIAM J. Numer. Anal 29 (1), 32-56, (1992).
    • (1992) SIAM J. Numer. Anal , vol.29 , Issue.1 , pp. 32-56
    • Nicolaides, R.A.1
  • 60
    • 0001777623 scopus 로고
    • Finite-difference approach to the Hodge theory of harmonic forms
    • J. Dodziuk, Finite-difference approach to the Hodge theory of harmonic forms, American Journal of Mathematics 98 (1), 79-104, (1973).
    • (1973) American Journal of Mathematics , vol.98 , Issue.1 , pp. 79-104
    • Dodziuk, J.1
  • 62
    • 0005288503 scopus 로고
    • American Mathematical Society, New York City
    • S. Lefschetz, Algebraic Topology, American Mathematical Society, New York City, (1942).
    • (1942) Algebraic Topology
    • Lefschetz, S.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.