메뉴 건너뛰기




Volumn 38, Issue 1, 2009, Pages 15-49

The discontinuous Galerkin method for two-dimensional hyperbolic problems part II: A posteriori error estimation

Author keywords

A posteriori error estimation; Discontinuous Galerkin method; Hyperbolic problems; Superconvergence

Indexed keywords

A POSTERIORI ERROR ESTIMATION; BASIS FUNCTIONS; DISCONTINUOUS FINITE ELEMENTS; DISCONTINUOUS GALERKIN METHOD; DISCONTINUOUS SOLUTIONS; DISCRETIZATION ERRORS; FINITE ELEMENT SPACES; FIRST ORDERS; GALERKIN; GLOBAL SUPERCONVERGENCE; HYPERBOLIC PROBLEMS; LEADING TERMS; LINEAR AND NONLINEAR PROBLEMS; LOCAL PROBLEMS; MESH REFINEMENTS; PARTIAL DIFFERENTIALS; POSTERIORI ERROR ESTIMATES; SUPERCONVERGENCE; TRIANGULAR MESHES; TWO-DIMENSIONAL;

EID: 59349090599     PISSN: 08857474     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10915-008-9222-8     Document Type: Article
Times cited : (39)

References (35)
  • 2
    • 34548401244 scopus 로고    scopus 로고
    • The discontinuous Galerkin method for two-dimensional hyperbolic problems Part I: Superconvergence error analysis
    • S. Adjerid M. Baccouch 2007 The discontinuous Galerkin method for two-dimensional hyperbolic problems Part I: Superconvergence error analysis J. Sci. Comput. 33 75 113
    • (2007) J. Sci. Comput. , vol.33 , pp. 75-113
    • Adjerid, S.1    Baccouch, M.2
  • 5
    • 17444406320 scopus 로고    scopus 로고
    • Superconvergence of discontinuous finite element solutions for transient convection-diffusion problems
    • S. Adjerid A. Klauser 2005 Superconvergence of discontinuous finite element solutions for transient convection-diffusion problems J. Sci. Comput. 22 5 24
    • (2005) J. Sci. Comput. , vol.22 , pp. 5-24
    • Adjerid, S.1    Klauser, A.2
  • 6
    • 0037147359 scopus 로고    scopus 로고
    • A posteriori discontinuous finite element error estimation for two-dimensional hyperbolic problems
    • S. Adjerid T.C. Massey 2002 A posteriori discontinuous finite element error estimation for two-dimensional hyperbolic problems Comput. Methods Appl. Mech. Eng. 191 5877 5897
    • (2002) Comput. Methods Appl. Mech. Eng. , vol.191 , pp. 5877-5897
    • Adjerid, S.1    Massey, T.C.2
  • 7
    • 33645910891 scopus 로고    scopus 로고
    • Superconvergence of discontinuous finite element solutions for nonlinear hyperbolic problems
    • S. Adjerid T.C. Massey 2006 Superconvergence of discontinuous finite element solutions for nonlinear hyperbolic problems Comput. Methods Appl. Mech. Eng. 195 3331 3346
    • (2006) Comput. Methods Appl. Mech. Eng. , vol.195 , pp. 3331-3346
    • Adjerid, S.1    Massey, T.C.2
  • 9
    • 4243855770 scopus 로고    scopus 로고
    • Adaptive error control in solving ordinary differential equations by the discontinuous Galerkin method
    • University of Heidelberg
    • Bottcher, K., Rannacher, R.: Adaptive error control in solving ordinary differential equations by the discontinuous Galerkin method. Tech. Report, University of Heidelberg (1996)
    • (1996) Tech. Report
    • Bottcher, K.1    Rannacher, R.2
  • 10
    • 0141569419 scopus 로고    scopus 로고
    • A superconvergence result for discontinuous Galerkin methods applied to elliptic problems
    • P. Castillo 2003 A superconvergence result for discontinuous Galerkin methods applied to elliptic problems Comput. Methods Appl. Mech. Eng. 192 4675 4685
    • (2003) Comput. Methods Appl. Mech. Eng. , vol.192 , pp. 4675-4685
    • Castillo, P.1
  • 11
    • 34547241273 scopus 로고    scopus 로고
    • Superconvergence of the numerical traces for discontinuous Galerkin and hybridized methods for convection-diffusion problems in one space dimension
    • F. Celiker B. Cockburn 2006 Superconvergence of the numerical traces for discontinuous Galerkin and hybridized methods for convection-diffusion problems in one space dimension Math. Comput. 76 67 96
    • (2006) Math. Comput. , vol.76 , pp. 67-96
    • Celiker, F.1    Cockburn, B.2
  • 13
    • 0002154319 scopus 로고    scopus 로고
    • Error estimates for finite element methods for nonlinear conservation laws
    • B. Cockburn P.A. Gremaud 1996 Error estimates for finite element methods for nonlinear conservation laws SIAM J. Numer. Anal. 33 522 554
    • (1996) SIAM J. Numer. Anal. , vol.33 , pp. 522-554
    • Cockburn, B.1    Gremaud, P.A.2
  • 15
    • 84966246413 scopus 로고
    • TVB Runge-Kutta local projection discontinuous Galerkin methods for scalar conservation laws II: General framework
    • B. Cockburn C.W. Shu 1989 TVB Runge-Kutta local projection discontinuous Galerkin methods for scalar conservation laws II: General framework Math. Comput. 52 411 435
    • (1989) Math. Comput. , vol.52 , pp. 411-435
    • Cockburn, B.1    Shu, C.W.2
  • 16
    • 0344393366 scopus 로고    scopus 로고
    • The local discontinuous Galerkin finite element method for convection-diffusion systems
    • B. Cockburn C.W. Shu 1998 The local discontinuous Galerkin finite element method for convection-diffusion systems SIAM J. Numer. Anal. 35 2240 2463
    • (1998) SIAM J. Numer. Anal. , vol.35 , pp. 2240-2463
    • Cockburn, B.1    Shu, C.W.2
  • 17
    • 84966254473 scopus 로고
    • Discontinuous Galerkin methods for ordinary differential equation
    • M. Delfour W. Hager F. Trochu 1981 Discontinuous Galerkin methods for ordinary differential equation Math. Comput. 154 455 473
    • (1981) Math. Comput. , vol.154 , pp. 455-473
    • Delfour, M.1    Hager, W.2    Trochu, F.3
  • 18
    • 0026371189 scopus 로고
    • Spectral methods on triangles and other domains
    • M. Dubiner 1991 Spectral methods on triangles and other domains J. Sci. Comput. 6 345 390
    • (1991) J. Sci. Comput. , vol.6 , pp. 345-390
    • Dubiner, M.1
  • 19
    • 0012733086 scopus 로고    scopus 로고
    • Adaptive discontinuous Galerkin finite element methods for nonlinear hyperbolic conservations laws
    • R. Hartmann P. Houston 2002 Adaptive discontinuous Galerkin finite element methods for nonlinear hyperbolic conservations laws SIAM J. Sci. Comput. 24 979 1004
    • (2002) SIAM J. Sci. Comput. , vol.24 , pp. 979-1004
    • Hartmann, R.1    Houston, P.2
  • 20
    • 0033436922 scopus 로고    scopus 로고
    • A posteriori error analysis for numerical approximations of Friedrichs systems
    • P. Houston J. Mackenzie E. Süli G. Warnecke 1999 A posteriori error analysis for numerical approximations of Friedrichs systems Numer. Math. 82 433 470
    • (1999) Numer. Math. , vol.82 , pp. 433-470
    • Houston, P.1    MacKenzie, J.2    Süli, E.3    Warnecke, G.4
  • 21
    • 33846255479 scopus 로고    scopus 로고
    • Energy norm a posteriori error estimation of hp-adaptive discontinuous Galerkin methods for elliptic problems
    • P. Houston D. Schötzau T. Wihler 2007 Energy norm a posteriori error estimation of hp-adaptive discontinuous Galerkin methods for elliptic problems Math. Models Methods Appl. Sci. 17 33 62
    • (2007) Math. Models Methods Appl. Sci. , vol.17 , pp. 33-62
    • Houston, P.1    Schötzau, D.2    Wihler, T.3
  • 22
    • 0025488567 scopus 로고
    • Adaptive finite element methods for diffusion and convection problems
    • C. Johnson 1990 Adaptive finite element methods for diffusion and convection problems Comput. Methods Appl. Mech. Eng. 82 301 322
    • (1990) Comput. Methods Appl. Mech. Eng. , vol.82 , pp. 301-322
    • Johnson, C.1
  • 23
    • 0027004931 scopus 로고
    • Adaptive finite element methods in computational mechanics
    • C. Johnson J. Hansbo 1992 Adaptive finite element methods in computational mechanics Comput. Methods Appl. Mech. Eng. 101 143 181
    • (1992) Comput. Methods Appl. Mech. Eng. , vol.101 , pp. 143-181
    • Johnson, C.1    Hansbo, J.2
  • 24
    • 84990662772 scopus 로고
    • Adaptive finite element methods for conservation laws
    • C. Johnson A. Szepessy 1995 Adaptive finite element methods for conservation laws Commun. Pure Appl. Math. 48 199 243
    • (1995) Commun. Pure Appl. Math. , vol.48 , pp. 199-243
    • Johnson, C.1    Szepessy, A.2
  • 26
    • 0037244453 scopus 로고    scopus 로고
    • Error estimation for discontinuous Galerkin solutions of two-dimensional hyperbolic problems
    • L. Krivodonova J.E. Flaherty 2003 Error estimation for discontinuous Galerkin solutions of two-dimensional hyperbolic problems Adv. Comput. Math. 19 57 71
    • (2003) Adv. Comput. Math. , vol.19 , pp. 57-71
    • Krivodonova, L.1    Flaherty, J.E.2
  • 29
    • 0026106576 scopus 로고
    • A note on the convergence of the discontinuous Galerkin method for scalar hyperbolic equation
    • T. Peterson 1991 A note on the convergence of the discontinuous Galerkin method for scalar hyperbolic equation SIAM J. Numer. Anal. 28 133 140
    • (1991) SIAM J. Numer. Anal. , vol.28 , pp. 133-140
    • Peterson, T.1
  • 30
    • 0041823208 scopus 로고    scopus 로고
    • A posteriori error estimates for a discontinuous Galerkin method applied to elliptic problems
    • B. Riviere M. Wheeler 2003 A posteriori error estimates for a discontinuous Galerkin method applied to elliptic problems Comput. Math. Appl. 46 143 163
    • (2003) Comput. Math. Appl. , vol.46 , pp. 143-163
    • Riviere, B.1    Wheeler, M.2
  • 31
    • 0002777656 scopus 로고    scopus 로고
    • An hp a-priori error analysis of the DG time-stepping method for initial value problems
    • D. Schötzau C. Schwab 2000 An hp a-priori error analysis of the DG time-stepping method for initial value problems Calcolo 37 207 232
    • (2000) Calcolo , vol.37 , pp. 207-232
    • Schötzau, D.1    Schwab, C.2
  • 32
    • 0034437086 scopus 로고    scopus 로고
    • Time discretization of parabolic problems by the hp-version of the discontinuous Galerkin finite element method
    • D. Schötzau C. Schwab 2000 Time discretization of parabolic problems by the hp-version of the discontinuous Galerkin finite element method SIAM J. Numer. Anal. 38 837 875
    • (2000) SIAM J. Numer. Anal. , vol.38 , pp. 837-875
    • Schötzau, D.1    Schwab, C.2
  • 34
    • 0002800857 scopus 로고    scopus 로고
    • Finite element methods for hyperbolic problems: A posteriori error analysis and adaptivity
    • Oxford University Press London
    • Süli, E., Houston, P.: Finite element methods for hyperbolic problems: a posteriori error analysis and adaptivity. In: Duff, I., Watson, G. (eds.) State of the Art in Numerical Analysis. Oxford University Press, London (1997)
    • (1997) State of the Art in Numerical Analysis
    • Süli, E.1    Houston, P.2    Duff, I.3    Watson, G.4


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.