메뉴 건너뛰기




Volumn 18, Issue 5, 2008, Pages 739-757

A construction of spaces of compatible differential forms on cellular complexes

Author keywords

Differential forms; Finite differences; Finite elements

Indexed keywords

FINITE DIFFERENCE METHOD; FINITE ELEMENT METHOD; MATHEMATICAL OPERATORS; TWO DIMENSIONAL;

EID: 44349178604     PISSN: 02182025     EISSN: None     Source Type: Journal    
DOI: 10.1142/S021820250800284X     Document Type: Article
Times cited : (47)

References (34)
  • 1
    • 14844327732 scopus 로고    scopus 로고
    • Differential complexes and numerical stability
    • Beijing, Higher Ed. Press
    • D. N. Arnold, Differential complexes and numerical stability, in Proc. of the International Congress of Mathematicians, Vol. I (Beijing, 2002) (Higher Ed. Press, 2002). pp. 137-157.
    • (2002) Proc. of the International Congress of Mathematicians , vol.1 , pp. 137-157
    • Arnold, D.N.1
  • 2
    • 33646721932 scopus 로고    scopus 로고
    • Finite element exterior calculus, homological techniques and applications
    • D. N. Arnold, R. S. Falk and R. Winther, Finite element exterior calculus, homological techniques and applications, Acta Numer. 15 (2006) 1-155.
    • (2006) Acta Numer , vol.15 , pp. 1-155
    • Arnold, D.N.1    Falk, R.S.2    Winther, R.3
  • 3
    • 0036768154 scopus 로고    scopus 로고
    • Mixed finite elements for elasticity
    • D. N. Arnold and R. Winther, Mixed finite elements for elasticity, Numer. Math. 92 (2002) 401-419.
    • (2002) Numer. Math , vol.92 , pp. 401-419
    • Arnold, D.N.1    Winther, R.2
  • 4
    • 44349168074 scopus 로고    scopus 로고
    • P. B. Bochev and J. M. Hyman, Principles of Mimetic Discretizations of Differential Operators, IMA Math. Appl., 142 (Springer, 2006), pp. 89-119.
    • P. B. Bochev and J. M. Hyman, Principles of Mimetic Discretizations of Differential Operators, IMA Vol. Math. Appl., Vol. 142 (Springer, 2006), pp. 89-119.
  • 6
    • 0003285219 scopus 로고
    • Differential Forms in Algebraic Topology
    • Springer-Verlag
    • R. Bott and L. W. Tu, Differential Forms in Algebraic Topology, Graduate Texts in Mathematics, Vol. 82 (Springer-Verlag. 1982).
    • (1982) Graduate Texts in Mathematics , vol.82
    • Bott, R.1    Tu, L.W.2
  • 8
    • 25144443045 scopus 로고    scopus 로고
    • A family of mimetic finite difference methods on polygonal and polyhedral meshes
    • F. Brezzi, K. Lipnikov and V. Simoncini, A family of mimetic finite difference methods on polygonal and polyhedral meshes, Math. Mod. Meth. Appl. Sci. 15 (2005) 1533-1551.
    • (2005) Math. Mod. Meth. Appl. Sci , vol.15 , pp. 1533-1551
    • Brezzi, F.1    Lipnikov, K.2    Simoncini, V.3
  • 9
    • 15344344066 scopus 로고    scopus 로고
    • A dual finite element complex on the barycentric refinement
    • A. Buffa and S. H. Christiansen, A dual finite element complex on the barycentric refinement, C. R. Math. Acad. Sci. Paris 340 (2005) 461-464.
    • (2005) C. R. Math. Acad. Sci. Paris , vol.340 , pp. 461-464
    • Buffa, A.1    Christiansen, S.H.2
  • 10
    • 11244320532 scopus 로고    scopus 로고
    • A characterization of second order differential operators on finite element spaces
    • S. H. Christiansen, A characterization of second order differential operators on finite element spaces, Math. Mod. Meth. Appl. Sci.14 (2004) 1881-1892.
    • (2004) Math. Mod. Meth. Appl. Sci , vol.14 , pp. 1881-1892
    • Christiansen, S.H.1
  • 11
    • 34547256262 scopus 로고    scopus 로고
    • Stability of Hodge decompositions in finite element spaces of differential forms in arbitrary dimension
    • S. H. Christiansen, Stability of Hodge decompositions in finite element spaces of differential forms in arbitrary dimension, Numer. Math. 107 (2007) 87-106.
    • (2007) Numer. Math , vol.107 , pp. 87-106
    • Christiansen, S.H.1
  • 12
    • 42349110974 scopus 로고    scopus 로고
    • Smoothed projections in finite element exterior calculus
    • S. H. Christiansen and R. Winther. Smoothed projections in finite element exterior calculus, Math. Comp. 77 (2008) 813-829.
    • (2008) Math. Comp , vol.77 , pp. 813-829
    • Christiansen, S.H.1    Winther, R.2
  • 13
    • 0002214041 scopus 로고
    • Maximum principle and uniform convergence for the finite element method
    • P. G. Ciarlet and P.-A. Raviart, Maximum principle and uniform convergence for the finite element method, Comput. Meth. Appl. Mech. Engrg. 2 (1973) 17-31.
    • (1973) Comput. Meth. Appl. Mech. Engrg , vol.2 , pp. 17-31
    • Ciarlet, P.G.1    Raviart, P.-A.2
  • 17
    • 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
  • 19
    • 26944434183 scopus 로고    scopus 로고
    • Convergence analysis and error estimates for mixed finite element method on distorted meshes
    • Y. Kuznetsov and S. Repin, Convergence analysis and error estimates for mixed finite element method on distorted meshes, J. Numer. Math. 13 (2005) 33-51.
    • (2005) J. Numer. Math , vol.13 , pp. 33-51
    • Kuznetsov, Y.1    Repin, S.2
  • 21
    • 0012783530 scopus 로고    scopus 로고
    • Revised 3rd edn, Springer
    • S. Lang, Algebra, Revised 3rd edn. (Springer, 2002).
    • (2002) Algebra
    • Lang, S.1
  • 24
    • 0001175293 scopus 로고
    • A mixed finite element method for 2nd order elliptic problems
    • Mathematical Aspects of the Finite Element Method, eds. I. Galligani and E. Magenes, Springer-Verlag
    • P. A. Raviart and J.-M. Thomas, A mixed finite element method for 2nd order elliptic problems, Mathematical Aspects of the Finite Element Method, Lecture Notes in Math., eds. I. Galligani and E. Magenes, Vol. 606 (Springer-Verlag, 1977), pp. 292-315.
    • (1977) Lecture Notes in Math , vol.606 , pp. 292-315
    • Raviart, P.A.1    Thomas, J.-M.2
  • 25
    • 44349084019 scopus 로고    scopus 로고
    • G. De R.ham, Variétés Différentiables. Formes, Courants, Formes Harmoniques, Troisième edn. Publications de I'Institut de Mathématique de FUniversité de Nancago, III. Actualités Scientifiques et industrielles, No. 1222b (Hermann, 1973).
    • G. De R.ham, Variétés Différentiables. Formes, Courants, Formes Harmoniques, Troisième edn. Publications de I'Institut de Mathématique de FUniversité de Nancago, III. Actualités Scientifiques et industrielles, No. 1222b (Hermann, 1973).
  • 26
    • 70350630547 scopus 로고    scopus 로고
    • J. E. Roberts and J.-M. Thomas, Mixed and hybrid methods, 523-640, in Handbook of Numerical Analysis. II, Finite Element Methods (Part 1), eds. P. G. Ciarlet and J.-L. Lions (North-Holland, 1991).
    • J. E. Roberts and J.-M. Thomas, Mixed and hybrid methods, 523-640, in Handbook of Numerical Analysis. Vol. II, Finite Element Methods (Part 1), eds. P. G. Ciarlet and J.-L. Lions (North-Holland, 1991).
  • 28
    • 0034159461 scopus 로고    scopus 로고
    • Stable FEM-FDTD hybrid method for Maxwell's equations
    • T. Rylander and A. Bondeson, Stable FEM-FDTD hybrid method for Maxwell's equations, Comput. Phys. Comm. 125 (2000) 75-82.
    • (2000) Comput. Phys. Comm , vol.125 , pp. 75-82
    • Rylander, T.1    Bondeson, A.2
  • 29
    • 20444493930 scopus 로고    scopus 로고
    • High order Nédélec elements with local complete sequence properties
    • J. Schöberl and S. Zaglmayr, High order Nédélec elements with local complete sequence properties, COMPEL 24 (2005) 374-384.
    • (2005) COMPEL , vol.24 , pp. 374-384
    • Schöberl, J.1    Zaglmayr, S.2
  • 30
    • 42349100577 scopus 로고    scopus 로고
    • A posteriori, error estimates for Maxwell equations
    • J. Schöberl, A posteriori, error estimates for Maxwell equations, Math. Comp. 77 (2008) 633-649.
    • (2008) Math. Comp , vol.77 , pp. 633-649
    • Schöberl, J.1
  • 32
    • 44349095605 scopus 로고    scopus 로고
    • M. Taylor, Partial Differential Equations, I Basic Theory (Springer-Verlag, 1996).
    • M. Taylor, Partial Differential Equations, Vol. I Basic Theory (Springer-Verlag, 1996).
  • 33
    • 51249194378 scopus 로고
    • Sur les théorèmes de De Rham
    • A. Weil, Sur les théorèmes de De Rham, Comment. Math. Helv. 26 (1952) 119-145.
    • (1952) Comment. Math. Helv , vol.26 , pp. 119-145
    • Weil, A.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.