메뉴 건너뛰기




Volumn 11, Issue 4, 2003, Pages 253-287

Stability and convergence of mixed discontinuous finite element methods for second-order differential problems

Author keywords

Characteristics; Convergence; Error estimates; Mixed discontinuous finite element methods; Second order problems; Stability

Indexed keywords

ASYMPTOTIC STABILITY; BOUNDARY CONDITIONS; CONVERGENCE OF NUMERICAL METHODS; ERROR ANALYSIS; GALERKIN METHODS; GREEN'S FUNCTION; LAGRANGE MULTIPLIERS; PARTIAL DIFFERENTIAL EQUATIONS; POLYNOMIALS; THEOREM PROVING; VECTORS;

EID: 0346361568     PISSN: 15702820     EISSN: None     Source Type: Journal    
DOI: 10.1163/156939503322663449     Document Type: Article
Times cited : (12)

References (21)
  • 2
    • 0000439432 scopus 로고
    • A characteristics-mixed finite element for advection-dominated transport problems
    • T. Arbogast and M. F. Wheeler, A characteristics-mixed finite element for advection-dominated transport problems. SIAM J. Numer. Anal. (1995) 32, 404-424.
    • (1995) SIAM J. Numer. Anal. , vol.32 , pp. 404-424
    • Arbogast, T.1    Wheeler, M.F.2
  • 3
    • 0001804939 scopus 로고
    • Mixed and nonconforming finite element methods: Implementation, postprocessing and error estimates
    • D. N. Arnold and F. Breezi, Mixed and nonconforming finite element methods: implementation, postprocessing and error estimates. RAIRO Modèl. Math. Anal. Numér. (1985) 19, 7-32.
    • (1985) RAIRO Modèl. Math. Anal. Numér , vol.19 , pp. 7-32
    • Arnold, D.N.1    Breezi, F.2
  • 4
    • 0036410391 scopus 로고    scopus 로고
    • Unified analysis of discontinuous Galerkin methods for elliptic problems
    • D.N. Arnold, F. Breezi, B. Cockburn, and L.D. Marini, Unified analysis of discontinuous Galerkin methods for elliptic problems. SIAM J. Numer. Anal. (2001) 39, 1749-1779.
    • (2001) SIAM J. Numer. Anal. , vol.39 , pp. 1749-1779
    • Arnold, D.N.1    Breezi, F.2    Cockburn, B.3    Marini, L.D.4
  • 5
    • 0001416032 scopus 로고    scopus 로고
    • A high-order accurate discontinuous finite element method for the numerical solution of the compressible Navier-Stokes equations
    • F. Bassi and S. Rebay, A high-order accurate discontinuous finite element method for the numerical solution of the compressible Navier-Stokes equations. J. Comp. Phys. (1997) 131, 267-279.
    • (1997) J. Comp. Phys. , vol.131 , pp. 267-279
    • Bassi, F.1    Rebay, S.2
  • 6
    • 0003199785 scopus 로고
    • Mixed finite elements for second order elliptic problems in three variables
    • F. Brezzi, J. Douglas, Jr., R. Durán, and M. Fortin, Mixed finite elements for second order elliptic problems in three variables. Numer. Math. (1987) 51, 237-250.
    • (1987) Numer. Math. , vol.51 , pp. 237-250
    • Brezzi, F.1    Douglas Jr., J.2    Durán, R.3    Fortin, M.4
  • 8
    • 34250118577 scopus 로고
    • Two families of mixed finite elements for second order elliptic problems
    • F. Brezzi, J. Douglas, Jr., and L.D. Marini, Two families of mixed finite elements for second order elliptic problems. Numer. Math. (1985) 47, 217-235.
    • (1985) Numer. Math. , vol.47 , pp. 217-235
    • Brezzi, F.1    Douglas Jr., J.2    Marini, L.D.3
  • 10
    • 0038271897 scopus 로고    scopus 로고
    • Numerical study of the hp version of mixed discontinuous finite element methods for reaction-diffusion problems: The 1D case
    • H. Chen, Z. Chen, and B. Li, Numerical study of the hp version of mixed discontinuous finite element methods for reaction-diffusion problems: the 1D case. Numer. Meth. Partial Diff. Equations (2003) 19, 525-553.
    • (2003) Numer. Meth. Partial Diff. Equations , vol.19 , pp. 525-553
    • Chen, H.1    Chen, Z.2    Li, B.3
  • 11
    • 0034930339 scopus 로고    scopus 로고
    • On the relationship of various discontinuous finite element methods for second-order elliptic equations
    • Z. Chen, On the relationship of various discontinuous finite element methods for second-order elliptic equations. East-West J. Numer. Math. (2001) 9, No. 2, 99-122.
    • (2001) East-West J. Numer. Math. , vol.9 , Issue.2 , pp. 99-122
    • Chen, Z.1
  • 12
    • 0037192724 scopus 로고    scopus 로고
    • Characteristic mixed discontinuous finite element methods for advection-dominated diffusion problems
    • Z. Chen, Characteristic mixed discontinuous finite element methods for advection-dominated diffusion problems. Comp. Meth. Appl. Mech. Engrg. (2002) 191, 2509-2538.
    • (2002) Comp. Meth. Appl. Mech. Engrg. , vol.191 , pp. 2509-2538
    • Chen, Z.1
  • 13
    • 51249179041 scopus 로고
    • Prismatic mixed finite elements for second order elliptic problems
    • Z. Chen and J. Douglas, Jr., Prismatic mixed finite elements for second order elliptic problems. Calcolo (1989) 26, 135-148.
    • (1989) Calcolo , vol.26 , pp. 135-148
    • Chen, Z.1    Douglas Jr., J.2
  • 14
    • 0141645575 scopus 로고    scopus 로고
    • Error analysis for characteristics-based methods for degenerate parabolic problems
    • Z. Chen, R. E. Ewing, E. Q. Jiang, and A.M., Spagnuolo, Error analysis for characteristics-based methods for degenerate parabolic problems. SIAM J. Numer. Anal. (2003) 40, 1491-1515.
    • (2003) SIAM J. Numer. Anal. , vol.40 , pp. 1491-1515
    • Chen, Z.1    Ewing, R.E.2    Jiang, E.Q.3    Spagnuolo, A.M.4
  • 15
    • 0025639748 scopus 로고
    • An Eulerian Lagrangian localized adjoint method for the advection-diffusion equation
    • M. A. Celia, T. F. Russell, I. Herrera, and R. E. Ewing, An Eulerian Lagrangian localized adjoint method for the advection-diffusion equation. Advances in Water Resources (1990) 13, 187-206.
    • (1990) Advances in Water Resources , vol.13 , pp. 187-206
    • Celia, M.A.1    Russell, T.F.2    Herrera, I.3    Ewing, R.E.4
  • 16
    • 0344393366 scopus 로고    scopus 로고
    • The local discontinuous Galerkin method for time-dependent convection-diffusion systems
    • B. Cockburn and C.-W. Shu, The local discontinuous Galerkin method for time-dependent convection-diffusion systems. SIAM J. Numer. Anal. (1998) 35, 2440-2463.
    • (1998) SIAM J. Numer. Anal. , vol.35 , pp. 2440-2463
    • Cockburn, B.1    Shu, C.-W.2
  • 17
    • 0000281250 scopus 로고
    • Some improved error estimates for the modified method of characteristics
    • C. N. Dawson, T. F. Russell, and M. F. Wheeler, Some improved error estimates for the modified method of characteristics. SIAM J. Numer. Anal. (1989) 26, 1487-1512.
    • (1989) SIAM J. Numer. Anal. , vol.26 , pp. 1487-1512
    • Dawson, C.N.1    Russell, T.F.2    Wheeler, M.F.3
  • 18
    • 0001235787 scopus 로고
    • Numerical methods for convection dominated diffusion problems based on combining the method of characteristics with finite element or finite difference procedures
    • J. Douglas, Jr. and T. F. Russell, Numerical methods for convection dominated diffusion problems based on combining the method of characteristics with finite element or finite difference procedures. SIAM J. Numer. Anal. (1982) 19, 871-885.
    • (1982) SIAM J. Numer. Anal. , vol.19 , pp. 871-885
    • Douglas Jr., J.1    Russell, T.F.2
  • 20
    • 0001175293 scopus 로고
    • A mixed finite element method for second order elliptic problems
    • Springer, Berlin
    • R. Raviart and J. Thomas, A mixed finite element method for second order elliptic problems. Lecture Notes in Mathematics, Vol. 606. Springer, Berlin, 1977, pp. 292-315.
    • (1977) Lecture Notes in Mathematics , vol.606 , pp. 292-315
    • Raviart, R.1    Thomas, J.2
  • 21
    • 0003630916 scopus 로고
    • Triangular mesh methods for the neutron transport equation
    • Tech. Report No. LA-UR-73-479, Los Alamos Scientific Laboratory
    • W. H. Reed and T. R. Hill, Triangular mesh methods for the neutron transport equation. Tech. Report No. LA-UR-73-479, Los Alamos Scientific Laboratory, 1973.
    • (1973)
    • Reed, W.H.1    Hill, T.R.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.