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Volumn 42, Issue 6, 2008, Pages 941-959

Inner products in covolume and mimetic methods

Author keywords

Compatible discretization; Covolume method; Discrete exact sequence; Discrete Helmholtz orthogonality; Mimetic method

Indexed keywords


EID: 55049089695     PISSN: 0764583X     EISSN: 12903841     Source Type: Journal    
DOI: 10.1051/m2an:2008030     Document Type: Article
Times cited : (12)

References (18)
  • 1
    • 14844327732 scopus 로고    scopus 로고
    • Differential complexes and numerical stability
    • Higher Ed. Press, Beijing
    • D.N. Arnold, Differential complexes and numerical stability, in Proceedings of the International Congress of Mathematicians, Vol. I, Higher Ed. Press, Beijing (2002) 137-157.
    • (2002) Proceedings of the International Congress of Mathematicians , vol.1 , pp. 137-157
    • Arnold, D.N.1
  • 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. East-West J. Numer. Math 9 (2001) 253-316.
    • (2001) East-West J. Numer. Math , vol.9 , pp. 253-316
    • Berndt, M.1    Lipnikov, K.2    Moulton, D.3    Shashkov, M.4
  • 3
    • 55049128197 scopus 로고    scopus 로고
    • P. Bochev and J.M. Hyman, Principles of mimetic discretizations of differential operators, in Compatible Spatial Discretizations, D. Arnold, P. Bochev, R. Lehoucq, R. Nicolaides and M. Shashkov Eds., IMA in Mathematics and its Applications 142, Springer, New York (2006).
    • P. Bochev and J.M. Hyman, Principles of mimetic discretizations of differential operators, in Compatible Spatial Discretizations, D. Arnold, P. Bochev, R. Lehoucq, R. Nicolaides and M. Shashkov Eds., IMA Volumes in Mathematics and its Applications 142, Springer, New York (2006).
  • 4
    • 0036493672 scopus 로고    scopus 로고
    • Generating whitney forms of polynomial degree one and higher
    • A. Bossavit, Generating whitney forms of polynomial degree one and higher. IEEE Trans. Magn. 38 (2002) 341-344.
    • (2002) IEEE Trans. Magn , vol.38 , pp. 341-344
    • Bossavit, A.1
  • 5
    • 0033461694 scopus 로고    scopus 로고
    • Canonical construction of finite elements
    • R. Hiptmair, Canonical construction of finite elements. Math. Comp. 68 (1999) 1325-1346.
    • (1999) Math. Comp , vol.68 , pp. 1325-1346
    • Hiptmair, R.1
  • 6
    • 1542355827 scopus 로고    scopus 로고
    • Ph.D. thesis, California Institute of Technology, USA
    • A. Hirani, Discrete Exterior Calculus. Ph.D. thesis, California Institute of Technology, USA (2003).
    • (2003) Discrete Exterior Calculus
    • Hirani, A.1
  • 7
    • 0031333803 scopus 로고    scopus 로고
    • The adjoint operators for the natural discretizations for the divergence, gradient, and curl on logically rectangular grids
    • J.M. Hyman and M. Shashkov, The adjoint operators for the natural discretizations for the divergence, gradient, and curl on logically rectangular grids. IMACS J. Appl. Num. Math. 25 (1997) 1-30.
    • (1997) IMACS J. Appl. Num. Math , vol.25 , pp. 1-30
    • Hyman, J.M.1    Shashkov, M.2
  • 8
    • 0031071242 scopus 로고    scopus 로고
    • Natural discretizations for the divergence, gradient, and curl on logically rectangular grids
    • J.M. Hyman and M. Shashkov, Natural discretizations for the divergence, gradient, and curl on logically rectangular grids. Comput. Math. Appl. 33 (1997) 81-104.
    • (1997) Comput. Math. Appl , vol.33 , pp. 81-104
    • Hyman, J.M.1    Shashkov, M.2
  • 9
    • 0000397429 scopus 로고    scopus 로고
    • Mimetic discretizations for Maxwell's equations
    • J.M. Hyman and M. Shashkov, Mimetic discretizations for Maxwell's equations. J. Comp. Phys. 151 (1999) 881-909.
    • (1999) J. Comp. Phys , vol.151 , pp. 881-909
    • Hyman, J.M.1    Shashkov, M.2
  • 10
    • 0002058288 scopus 로고    scopus 로고
    • The orthogonal decomposition theorems for mimetic finite difference methods
    • J.M. Hyman and M. Shashkov, The orthogonal decomposition theorems for mimetic finite difference methods. SIAM J. Numer. Anal. 36 (1999) 788-818.
    • (1999) SIAM J. Numer. Anal , vol.36 , pp. 788-818
    • Hyman, J.M.1    Shashkov, M.2
  • 11
    • 34250256485 scopus 로고
    • Mixed finite elements in R3
    • J.C. Nedelec, Mixed finite elements in R3. Numer. Math. 35 (1980) 315-341.
    • (1980) Numer. Math , vol.35 , pp. 315-341
    • Nedelec, J.C.1
  • 12
    • 34250103285 scopus 로고
    • A new family of mixed finite elements in R3
    • J.C. Nedelec, A new family of mixed finite elements in R3. Numer. Math. 50 (1986) 57-81.
    • (1986) Numer. Math , vol.50 , pp. 57-81
    • Nedelec, J.C.1
  • 13
    • 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 (1992) 32-56.
    • (1992) SIAM J. Numer. Anal , vol.29 , pp. 32-56
    • Nicolaides, R.A.1
  • 14
    • 55049090162 scopus 로고    scopus 로고
    • R. Nicolaides and K. Trapp, Covolume discretizations of differential forms, in Compatible Spatial Discretizations, D. Arnold, P. Bochev, R. Lehoucq, R. Nicolaides and M. Shashkov Eds., IMA in Mathematics and its Applications 142, Springer, New York (2006).
    • R. Nicolaides and K. Trapp, Covolume discretizations of differential forms, in Compatible Spatial Discretizations, D. Arnold, P. Bochev, R. Lehoucq, R. Nicolaides and M. Shashkov Eds., IMA Volumes in Mathematics and its Applications 142, Springer, New York (2006).
  • 15
    • 0032361315 scopus 로고    scopus 로고
    • Convergence analysis of a covolume scheme for Maxwell's equations in three dimensions
    • R.A. Nicolaides and D.Q. Wang, Convergence analysis of a covolume scheme for Maxwell's equations in three dimensions. Math. Comp. 67 (1998) 947-963.
    • (1998) Math. Comp , vol.67 , pp. 947-963
    • Nicolaides, R.A.1    Wang, D.Q.2
  • 16
    • 0001389991 scopus 로고    scopus 로고
    • Covolume solutions of three-dimensional div-curl equations
    • R.A. Nicolaides and X. Wu, Covolume solutions of three-dimensional div-curl equations. SIAM J. Numer. Anal. 34 (1997) 2195-2203.
    • (1997) SIAM J. Numer. Anal , vol.34 , pp. 2195-2203
    • Nicolaides, R.A.1    Wu, X.2
  • 17
    • 0005940504 scopus 로고    scopus 로고
    • A mixed finite elemnt method for second order elliptic problems
    • Springer-Verlag (1977) 292-315
    • P.A. Raviart and J.M. Thomas, A mixed finite elemnt method for second order elliptic problems, in Springer Lecture Notes in Mathematics 606, Springer-Verlag (1977) 292-315.
    • Springer Lecture Notes in Mathematics , vol.606
    • Raviart, P.A.1    Thomas, J.M.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.