메뉴 건너뛰기




Volumn 74, Issue 249, 2005, Pages 1-23

Failure of the discrete maximum principle for an elliptic finite element problem

Author keywords

Discrete maximum principle; Finite elements; Green's function

Indexed keywords


EID: 11244251108     PISSN: 00255718     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0025-5718-04-01651-5     Document Type: Article
Times cited : (101)

References (12)
  • 1
    • 0003957050 scopus 로고    scopus 로고
    • The mathematical theory of finite element methods, second ed
    • Springer-Verlag, New York. MR 2003a:65103
    • Susanne C. Brenner and L. Ridgway Scott, The mathematical theory of finite element methods, second ed., Texts in Applied Mathematics, vol. 15, Springer-Verlag, New York, 2002. MR 2003a:65103
    • (2002) Texts in Applied Mathematics , vol.15
    • Brenner, S.C.1    Scott, L.R.2
  • 2
    • 0002214041 scopus 로고
    • Maximum principle and uniform convergence for the finite element method
    • MR 51:11992
    • P. G. Ciarlet and P.-A. Raviart, Maximum principle and uniform convergence for the finite element method, Comput. Methods Appl. Mech. Engrg. 2 (1973), 17-31. MR 51:11992
    • (1973) Comput. Methods Appl. Mech. Engrg. , vol.2 , pp. 17-31
    • Ciarlet, P.G.1    Raviart, P.-A.2
  • 3
    • 0037376063 scopus 로고    scopus 로고
    • One-to-one piecewise linear mappings over triangulations
    • electronic
    • Michael S. Floater, One-to-one piecewise linear mappings over triangulations, Math. Comp. 72 (2003), no. 242, 685-696 (electronic).
    • (2003) Math. Comp. , vol.72 , Issue.242 , pp. 685-696
    • Floater, M.S.1
  • 4
    • 0019708039 scopus 로고
    • Some remarks on the discrete maximum-principle for finite elements of higher order
    • MR 83a:65109
    • W. Höhn and H.-D. Mittelmann, Some remarks on the discrete maximum-principle for finite elements of higher order, Computing 27 (1981), no. 2, 145-154. MR 83a:65109
    • (1981) Computing , vol.27 , Issue.2 , pp. 145-154
    • Höhn, W.1    Mittelmann, H.-D.2
  • 5
    • 0039248648 scopus 로고    scopus 로고
    • Weakened acute type condition for tetrahedral triangulations and the discrete maximum principle
    • (electronic). MR 20011:65126
    • Sergey Korotov, Michal Křížek, and Pekka Neittaanmäki, Weakened acute type condition for tetrahedral triangulations and the discrete maximum principle, Math. Comp. 70 (2001). no. 233, 107-119 (electronic). MR 20011:65126
    • (2001) Math. Comp. , vol.70 , Issue.233 , pp. 107-119
    • Korotov, S.1    Křížek, M.2    Neittaanmäki, P.3
  • 6
    • 84972488101 scopus 로고
    • Criteria for positive Green's functions
    • MR 37:4400
    • Kurt Kreith, Criteria for positive Green's functions, Illinois, 1. Math. 12 (1968), 475-478. MR 37:4400
    • (1968) Illinois, 1. Math. , vol.12 , pp. 475-478
    • Kreith, K.1
  • 7
    • 0040737841 scopus 로고
    • On the strong maximum principle for some piecewise linear finite element approximate problems of nonpositive type
    • MR 84b:65118
    • Vitoriano Ruas Santos, On the strong maximum principle for some piecewise linear finite element approximate problems of nonpositive type, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 29 (1982), no. 2, 473-491. MR 84b:65118
    • (1982) J. Fac. Sci. Univ. Tokyo Sect. IA Math. , vol.29 , Issue.2 , pp. 473-491
    • Santos, V.R.1
  • 8
    • 84966242339 scopus 로고
    • ∞ on plane polygonal domains. I
    • MR, 81e:65063
    • ∞ on plane polygonal domains. I, Math. Comp. 34 (1980), no. 149, 77-91. MR, 81e:65063
    • (1980) Math. Comp. , vol.34 , Issue.149 , pp. 77-91
    • Schatz, A.H.1
  • 9
    • 84966250424 scopus 로고
    • ∞ estimates for the finite element method on irregular meshes
    • MR 55:9560
    • ∞ estimates for the finite element method on irregular meshes, Math. Comp. 30 (1976), no. 136, 681-697. MR 55:9560
    • (1976) Math. Comp. , vol.30 , Issue.136 , pp. 681-697
    • Scott, R.1
  • 10
    • 0003552714 scopus 로고
    • Prentice-Hall Inc., Englewood Cliffs, N. J., Prentice-Hall Series in Automatic Computation. MR 56:1747
    • Gilbert Strang and George J. Fix, An analysis of the finite element method, Prentice-Hall Inc., Englewood Cliffs, N. J., 1973, Prentice-Hall Series in Automatic Computation. MR 56:1747
    • (1973) An Analysis of the Finite Element Method
    • Strang, G.1    Fix, G.J.2
  • 11
    • 0003943048 scopus 로고    scopus 로고
    • Matrix iterative analysis, expanded ed.
    • Springer-Verlag, Berlin. MR 2001g:65002
    • Richard S. Varga, Matrix iterative analysis, expanded ed., Springer Series in Computational Mathematics, vol. 27, Springer-Verlag, Berlin, 2000. MR 2001g:65002
    • (2000) Springer Series in Computational Mathematics , vol.27
    • Varga, R.S.1
  • 12
    • 0033450269 scopus 로고    scopus 로고
    • A monotone finite element scheme for convection-diffusion equations
    • MR 99m:65225
    • Jinchao Xu and Ludmil Zikatanov, A monotone finite element scheme for convection-diffusion equations, Math. Comp. 68 (1999), no. 228, 1429-1446. MR 99m:65225
    • (1999) Math. Comp. , vol.68 , Issue.228 , pp. 1429-1446
    • Xu, J.1    Zikatanov, L.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.