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Volumn 80, Issue 275, 2011, Pages 1335-1367

Discontinuous Galerkin error estimation for linear symmetrizable hyperbolic systems

Author keywords

A posteriori error estimation; Discontinuous Galerkin method; Friedrichs symmetrizable systems; Linear hyperbolic systems; Superconvergence

Indexed keywords


EID: 79955674109     PISSN: 00255718     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0025-5718-2011-02460-9     Document Type: Article
Times cited : (28)

References (27)
  • 2
    • 34548401244 scopus 로고    scopus 로고
    • The discontinuous Galerkin method for two-dimensional hyperbolic problems Part I: Superconvergence error analysis
    • S. Adjerid and M. Baccouch, The discontinuous Galerkin method for two-dimensional hyperbolic problems Part I: Superconvergence error analysis, Journal of Scientific Computing 33 (2007), 75-113.
    • (2007) Journal of Scientific Computing , vol.33 , pp. 75-113
    • Adjerid, S.1    Baccouch, M.2
  • 4
    • 59349090599 scopus 로고    scopus 로고
    • The discontinuous Galerkin method for two-dimensional hyperbolic problems Part II: A Posteriori error estimation
    • S. Adjerid, The discontinuous Galerkin method for two-dimensional hyperbolic problems Part II: A Posteriori error estimation, Journal of Scientifc Computing 38 (2009), 15-49.
    • (2009) Journal of Scientifc Computing , vol.38 , pp. 15-49
    • Adjerid, S.1
  • 6
    • 0037147359 scopus 로고    scopus 로고
    • A posteriori discontinuous finite element error estimation for two-dimensional hyperbolic problems
    • S. Adjerid and T. C. Massey, A posteriori discontinuous finite element error estimation for two-dimensional hyperbolic problems, Computer Methods in Applied Mechanics and Engineering 191 (2002), 5877-5897.
    • (2002) Computer Methods in Applied Mechanics and Engineering , 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, Superconvergence of discontinuous finite element solutions for nonlinear hyperbolic problems, Computer Methods in Applied Mechanics and Engineering 195 (2006), 3331-3346.
    • (2006) Computer Methods in Applied Mechanics and Engineering , vol.195 , pp. 3331-3346
    • Adjerid, S.1
  • 9
    • 67949124645 scopus 로고    scopus 로고
    • Discontinuous Galerkin error estimation for linear symmetric hyperbolic systems
    • S. Adjerid, Discontinuous Galerkin error estimation for linear symmetric hyperbolic systems, Computer Methods in Applied Mechanics and Engineering 198 (2009), 3113-3129.
    • (2009) Computer Methods in Applied Mechanics and Engineering , vol.198 , pp. 3113-3129
    • Adjerid, S.1
  • 12
    • 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, Journal of Computational Physics 227 (2008), 9612-9627.
    • (2008) Journal of Computational Physics , vol.227 , pp. 9612-9627
    • Cheng, Y.1    Shu, C.-W.2
  • 13
    • 67349095629 scopus 로고    scopus 로고
    • Superconvergence of local discontinuous Galerkin methods for one-dimensional convection-diffusion equations
    • Y. Cheng, Superconvergence of local discontinuous Galerkin methods for one-dimensional convection-diffusion equations, Computers & Structures 87 (2009), 630-641.
    • (2009) Computers & Structures , vol.87 , pp. 630-641
    • Cheng, Y.1
  • 14
    • 77649102847 scopus 로고    scopus 로고
    • Superconvergence of discontinuous Galerkin and local discontinuous galerkin schemes for linear hyperbolic and convection-diffusion equations in one space dimension
    • Y. Cheng, Superconvergence of discontinuous Galerkin and local discontinuous galerkin schemes for linear hyperbolic and convection-diffusion equations in one space dimension, SIAM Journal on Numerical Analysis 47 (2010), 4044-4072.
    • (2010) SIAM Journal on Numerical Analysis , vol.47 , pp. 4044-4072
    • Cheng, Y.1
  • 15
    • 0006232594 scopus 로고    scopus 로고
    • A simple introduction to error estimation for nonlinear hyperbolic conservation laws
    • The Graduate Student's Guide for Numerical Analysis, (Berlin), Springer
    • B. Cockburn, A simple introduction to error estimation for nonlinear hyperbolic conservation laws, Proceedings of the 1998 EPSRC Summer School in Numerical Analysis, SSCM, volume 26 of the Graduate Student's Guide for Numerical Analysis, pages 1-46 (Berlin), Springer, 1999.
    • (1999) Proceedings of the 1998 EPSRC Summer School in Numerical Analysis, SSCM , vol.26 , pp. 1-46
    • Cockburn, B.1
  • 16
    • 0002154319 scopus 로고    scopus 로고
    • Error estimates for finite element methods for nonlinear conservation laws
    • B. Cockburn and P. A. Gremaud, Error estimates for finite element methods for nonlinear conservation laws, SIAM Journal on Numerical Analysis 33 (1996), 522-554.
    • (1996) SIAM Journal on Numerical Analysis , vol.33 , pp. 522-554
    • Cockburn, B.1    Gremaud, P.A.2
  • 17
    • 84966261380 scopus 로고
    • TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws IV: The multidimensional case
    • B. Cockburn, S. Hou, and C. W. Shu, TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws IV: The multidimensional case, Math. Comp. 54 (1990), 545-581.
    • (1990) Math. Comp. , vol.54 , pp. 545-581
    • Cockburn, B.1    Hou, S.2    Shu, C.W.3
  • 18
    • 45249130080 scopus 로고
    • TVB Runge-Kutta local projection discontinuous Galerkin methods of scalar conservation laws III: One dimensional systems
    • B. Cockburn, S. Y. Lin, and C. W. Shu, TVB Runge-Kutta local projection discontinuous Galerkin methods of scalar conservation laws III: One dimensional systems, Journal of Computational Physics 84 (1989), 90-113.
    • (1989) Journal of Computational Physics , vol.84 , pp. 90-113
    • Cockburn, B.1    Lin, S.Y.2    Shu, C.W.3
  • 19
    • 0000869912 scopus 로고
    • The Runge-Kutta local projection p1-discontinuous Galerkin method for scalar conservation laws
    • B. Cockburn and C. W. Shu, The Runge-Kutta local projection p1-discontinuous Galerkin method for scalar conservation laws, RAIROMod́el. Math. Anal. Nuḿer. 25 (1991), 337-361.
    • (1991) RAIROMod́el. Math. Anal. Numér. , vol.25 , pp. 337-361
    • Cockburn, B.1    Shu, C.W.2
  • 21
    • 0012733086 scopus 로고    scopus 로고
    • Adaptive discontinuous Galerkin finite element methods for nonlinear hyperbolic conservations laws
    • R. Hartmann and P. Houston, Adaptive discontinuous Galerkin finite element methods for nonlinear hyperbolic conservations laws, SIAM J. Sci. Comput. 24 (2002), 979-1004.
    • (2002) SIAM J. Sci. Comput. , vol.24 , pp. 979-1004
    • Hartmann, R.1    Houston, P.2
  • 22
    • 0037244453 scopus 로고    scopus 로고
    • Error estimation for discontinuous Galerkin solutions of two-dimensional hyperbolic problems
    • L. Krivodonova and J. E. Flaherty., Error estimation for discontinuous Galerkin solutions of two-dimensional hyperbolic problems, Advances in Computational Mathematics 19 (2003), 57-71.
    • (2003) Advances in Computational Mathematics , vol.19 , pp. 57-71
    • Krivodonova, L.1    Flaherty, J.E.2
  • 23
    • 0000451632 scopus 로고    scopus 로고
    • A posteriori error estimation for adaptive discontinuous Galerkin approximation of hyperbolic systems
    • (Berlin) (B. Cockburn, G. E. Karniadakis, and C. W. Shu, eds.), Springer
    • M. Larson and T. Barth, A posteriori error estimation for adaptive discontinuous Galerkin approximation of hyperbolic systems, Proc. International Symposium on Discontinuous Galerkin Methods Theory, Computation and Applications (Berlin) (B. Cockburn, G. E. Karniadakis, and C. W. Shu, eds.), Springer, 2000.
    • (2000) Proc. International Symposium on Discontinuous Galerkin Methods Theory, Computation and Applications
    • Larson, M.1    Barth, T.2
  • 26
    • 0009708499 scopus 로고
    • A representation of the Drazin inverse and characterizations of the index
    • Uriel G. Rothblum, A representation of the Drazin inverse and characterizations of the index, SIAM Journal on Applied Mathematics 31 (1976), no. 4, 646-648.
    • (1976) SIAM Journal on Applied Mathematics , vol.31 , Issue.4 , pp. 646-648
    • Rothblum, U.G.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.