메뉴 건너뛰기




Volumn 47, Issue 6, 2010, Pages 4044-4072

Superconvergence of discontinuous galerkin and local discontinuous galerkin schemes for linear hyperbolic and convection-diffusion equations in one space dimension

Author keywords

Discontinuous Galerkin method; Error estimates; Local discontinuous Galerkin method; Projection; Superconvergence; Upwind flux

Indexed keywords

DISCONTINUOUS GALERKIN METHODS; ERROR ESTIMATES; LOCAL DISCONTINUOUS GALERKIN METHOD; PROJECTION; SUPER-CONVERGENCE;

EID: 77649102847     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/090747701     Document Type: Article
Times cited : (135)

References (18)
  • 1
    • 0037016628 scopus 로고    scopus 로고
    • A posteriori error estimation for discontinuous Galerkin solutions of hyperbolic problems
    • DOI 10.1016/S0045-7825(01)00318-8, PII S0045782501003188
    • S. ADJERID, K. DEVINE, J. FLAHERTY, AND L. KRIVODONOVA, A posteriori error estimation for discontinuous Galerkin solutions of hyperbolic problems, Comput. Methods Appl. Mech. Engrg., 191 (2002), pp. 1097-1112. (Pubitemid 34102680)
    • (2002) Computer Methods in Applied Mechanics and Engineering , vol.191 , Issue.11-12 , pp. 1097-1112
    • Adjerid, S.1    Devine, K.D.2    Flaherty, J.E.3    Krivodonova, L.4
  • 3
    • 17444406320 scopus 로고    scopus 로고
    • Superconvergence of discontinuous finite element solutions for transient convection-diffusion problems
    • S. ADJERID AND A. KLAUSER, Superconvergence of discontinuous finite element solutions for transient convection-diffusion problems, J. Sci. Comput., 22/23 (2005), pp. 5-24.
    • (2005) J. Sci. Comput. , vol.22-23 , pp. 5-24
    • Adjerid, S.1    Klauser, A.2
  • 4
    • 33645910891 scopus 로고    scopus 로고
    • Superconvergence of discontinuous Galerkin solutions for a nonlinear scalar hyperbolic problem
    • S. ADJERID AND T. MASSEY, Superconvergence of discontinuous Galerkin solutions for a nonlinear scalar hyperbolic problem, Comput. Methods Appl. Mech. Engrg., 195 (2006), pp.3331-3346.
    • (2006) Comput. Methods Appl. Mech. Engrg. , vol.195 , pp. 3331-3346
    • Adjerid, S.1    Massey, T.2
  • 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. Comput. Phys., 131 (1997), pp. 267-279.
    • (1997) J. Comput. Phys. , vol.131 , pp. 267-279
    • Bassi, F.1    Rebay, S.2
  • 6
    • 0141569419 scopus 로고    scopus 로고
    • A superconvergence result for discontinuous Galerkin methods applied to elliptic problems
    • P. CASTILLO, A superconvergence result for discontinuous Galerkin methods applied to elliptic problems, Comput. Methods Appl. Mech. Engrg., 192 (2003), pp. 4675-4685.
    • (2003) Comput. Methods Appl. Mech. Engrg. , vol.192 , pp. 4675-4685
    • Castillo, P.1
  • 7
    • 34547241273 scopus 로고    scopus 로고
    • Superconvergence of the numerical traces of discontinuous Galerkin and hybridized methods for convection-diffusion problems in one space dimension
    • F. CELIKER AND B. COCKBURN, Superconvergence of the numerical traces of discontinuous Galerkin and hybridized methods for convection-diffusion problems in one space dimension, Math. Comp., 76 (2007), pp. 67-96.
    • (2007) Math. Comp. , vol.76 , pp. 67-96
    • Celiker, F.1    Cockburn, B.2
  • 8
    • 52749083843 scopus 로고    scopus 로고
    • Superconvergence and time evolution of discontinuous Galerkin finite element solutions
    • Y. CHENG AND C.-W. SHU, Superconvergence and time evolution of discontinuous Galerkin finite element solutions, J. Comput. Phys., 227 (2008), pp. 9612-9627.
    • (2008) J. Comput. Phys. , vol.227 , pp. 9612-9627
    • Cheng, Y.1    Shu, C.-W.2
  • 9
    • 67349095629 scopus 로고    scopus 로고
    • Superconvergence of local discontinuous Galerkin methods for convection-diffusion equations
    • Y. CHENG AND C.-W. SHU, Superconvergence of local discontinuous Galerkin methods for convection-diffusion equations, Computers and Structures, 87 (2009), pp. 630-641.
    • (2009) Computers and Structures , vol.87 , pp. 630-641
    • Cheng, Y.1    Shu, C.-W.2
  • 11
    • 84966261380 scopus 로고
    • The Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws IV: The multidimensional case
    • B. COCKBURN, S. HOU, AND C.-W. SHU, The Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws IV: The multidimensional case, Math. Comp., 54 (1990), pp. 545-581.
    • (1990) Math. Comp. , vol.54 , pp. 545-581
    • Cockburn, B.1    Hou, S.2    Shu, C.-W.3
  • 12
    • 45249130080 scopus 로고
    • TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws III: One dimensional systems
    • B. COCKBURN, S.-Y. LIN, AND C.-W. SHU, TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws III: One dimensional systems, J. Comput. Phys., 84 (1989), pp. 90-113.
    • (1989) J. Comput. Phys. , vol.84 , pp. 90-113
    • Cockburn, B.1    Lin, S.-Y.2    Shu, C.-W.3
  • 13
    • 84966246413 scopus 로고
    • TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws II: General framework
    • B. COCKBURN AND C.-W. SHU, TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws II: General framework, Math. Comp., 52 (1989), pp. 411-435.
    • (1989) Math. Comp. , vol.52 , pp. 411-435
    • Cockburn, B.1    Shu, C.-W.2
  • 14
    • 0000869912 scopus 로고
    • The Runge-Kutta local projection P1-discontinuous Galerkin finite element method for scalar conservation laws
    • B. COCKBURN AND C.-W. SHU, The Runge-Kutta local projection P1-discontinuous Galerkin finite element method for scalar conservation laws, RAIRO Modél. Math. Anal. Numér., 25 (1991), pp. 337-361.
    • (1991) RAIRO Modél. Math. Anal. Numér. , vol.25 , pp. 337-361
    • Cockburn, B.1    Shu, C.-W.2
  • 15
    • 0001690553 scopus 로고    scopus 로고
    • The Runge-Kutta Discontinuous Galerkin Method for Conservation Laws V: Multidimensional Systems
    • DOI 10.1006/jcph.1998.5892, PII S0021999198958922
    • B. COCKBURN AND C.-W. SHU, The Runge-Kutta discontinuous Galerkin method for conservation laws V: Multidimensional systems, J. Comput. Phys., 141 (1998), pp. 199-224. (Pubitemid 128344796)
    • (1998) Journal of Computational Physics , vol.141 , Issue.2 , pp. 199-224
    • Cockburn, B.1    Shu, C.-W.2
  • 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., 35 (1998), pp. 2440-2463. (Pubitemid 128464115)
    • (1998) SIAM Journal on Numerical Analysis , vol.35 , Issue.6 , pp. 2440-2463
    • Cockburn, B.1    Shu, C.-W.2
  • 17
    • 0000076512 scopus 로고    scopus 로고
    • Runge-Kutta Discontinuous Galerkin methods for convection-dominated problems
    • B. COCKBURN AND C.-W. SHU, Runge-Kutta discontinuous Galerkin methods for convectiondominated problems, J. Sci. Comput., 16 (2001), pp. 173-261. (Pubitemid 33818237)
    • (2001) Journal of Scientific Computing , vol.16 , Issue.3 , pp. 173-261
    • Cockburn, B.1    Shu, C.-W.2
  • 18
    • 18444370606 scopus 로고    scopus 로고
    • Error estimates to smooth solutions of Runge-Kutta discontinuous Galerkin methods for scalar conservation laws
    • Q. ZHANG AND C.-W. SHU, Error estimates to smooth solutions of Runge-Kutta discontinuous Galerkin methods for scalar conservation laws, SIAM J. Numer. Anal., 42 (2004), pp. 641-666.
    • (2004) SIAM J. Numer. Anal. , vol.42 , pp. 641-666
    • Zhang, Q.1    Shu, C.-W.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.