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Volumn 38, Issue 3, 2001, Pages 837-875

Time discretization of parabolic problems by the hp-version of the discontinuous Galerkin finite element method

Author keywords

Abstract parabolic problems; Discontinuous Galerkin methods; hp version of the finite element method

Indexed keywords


EID: 0034437086     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036142999352394     Document Type: Article
Times cited : (190)

References (41)
  • 1
    • 84985383836 scopus 로고
    • The hp-version of the finite element method for parabolic equations, I: The p-version in time
    • I. BABUŠKA AND T. JANIK, The hp-version of the finite element method for parabolic equations, I: The p-version in time, Numer. Methods Partial Differential Equations, 5 (1989), pp. 363-399.
    • (1989) Numer. Methods Partial Differential Equations , vol.5 , pp. 363-399
    • Babuška, I.1    Janik, T.2
  • 2
    • 84985305586 scopus 로고
    • The hp-version of the finite element method for parabolic equations, II: The hp-version in time
    • I. BABUŠKA AND T. JANIK, The hp-version of the finite element method for parabolic equations, II: The hp-version in time, Numer. Methods Partial Differential Equations, 6 (1990), pp. 343-369.
    • (1990) Numer. Methods Partial Differential Equations , vol.6 , pp. 343-369
    • Babuška, I.1    Janik, T.2
  • 3
    • 0028734274 scopus 로고
    • The p and hp-versions of the finite element method, basic principles and properties
    • I. BABUŠKA AND M. SURI, The p and hp-versions of the finite element method, basic principles and properties, SIAM Rev., 36 (1994), pp. 578-632.
    • (1994) SIAM Rev. , vol.36 , pp. 578-632
    • Babuška, I.1    Suri, M.2
  • 4
    • 84885255474 scopus 로고    scopus 로고
    • A discontinuous hp finite element method for convection diffusion problems
    • to appear
    • C.E. BAUMANN AND J.T. ODEN, A discontinuous hp finite element method for convection diffusion problems, Comput. Methods Appl. Mech. and Engrg., to appear.
    • Comput. Methods Appl. Mech. and Engrg.
    • Baumann, C.E.1    Oden, J.T.2
  • 6
    • 0002718851 scopus 로고    scopus 로고
    • Discontinuous Galerkin methods for convection dominated problems
    • High-Order Methods for Computational Physics, T.J. Barth and H. Deconinck, eds., Springer-Verlag, Berlin, 1999
    • B. COCKBURN, Discontinuous Galerkin methods for convection dominated problems, in High-Order Methods for Computational Physics, T.J. Barth and H. Deconinck, eds., Lect. Notes Comput. Sci. Eng. 9 (1999), Springer-Verlag, Berlin, 1999, pp. 69-224.
    • (1999) Lect. Notes Comput. Sci. Eng. , vol.9 , pp. 69-224
    • Cockburn, B.1
  • 7
    • 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.
    • (1998) SIAM J. Numer. Anal. , vol.35 , pp. 2440-2463
    • Cockburn, B.1    Shu, C.-W.2
  • 8
    • 84966254473 scopus 로고
    • Discontinuous Galerkin methods for ordinary differential equations
    • M. DELFOUR, W. HAGER, AND F. TROCHU, Discontinuous Galerkin methods for ordinary differential equations, Math. Comp., 36 (1981), pp. 455-473.
    • (1981) Math. Comp. , vol.36 , pp. 455-473
    • Delfour, M.1    Hager, W.2    Trochu, F.3
  • 9
    • 0026106415 scopus 로고
    • Adaptive finite element methods for parabolic problems I: A linear model problem
    • K. ERIKSSON AND C. JOHNSON, Adaptive finite element methods for parabolic problems I: A linear model problem, SIAM J. Numer. Anal., 28 (1991), pp. 43-77.
    • (1991) SIAM J. Numer. Anal. , vol.28 , pp. 43-77
    • Eriksson, K.1    Johnson, C.2
  • 11
    • 84904150653 scopus 로고
    • Adaptive finite element methods for parabolic problems IV: Nonlinear problems
    • K. ERIKSSON AND C. JOHNSON, Adaptive finite element methods for parabolic problems IV: Nonlinear problems, SIAM J. Numer. Anal., 32 (1995), pp. 1729-1749.
    • (1995) SIAM J. Numer. Anal. , vol.32 , pp. 1729-1749
    • Eriksson, K.1    Johnson, C.2
  • 12
    • 67649809189 scopus 로고
    • Adaptive finite element methods for parabolic problems V: Long-time integration
    • K. ERIKSSON AND C. JOHNSON, Adaptive finite element methods for parabolic problems V: Long-time integration, SIAM J. Numer. Anal., 32 (1995), pp. 1750-1763.
    • (1995) SIAM J. Numer. Anal. , vol.32 , pp. 1750-1763
    • Eriksson, K.1    Johnson, C.2
  • 13
    • 0001648207 scopus 로고    scopus 로고
    • Adaptive finite element methods for parabolic problems VI: Analytic semigroups
    • K. ERIKSSON, C. JOHNSON, AND S. LARSSON, Adaptive finite element methods for parabolic problems VI: Analytic semigroups, SIAM J. Numer. Anal., 35 (1998), pp. 1315-1325.
    • (1998) SIAM J. Numer. Anal. , vol.35 , pp. 1315-1325
    • Eriksson, K.1    Johnson, C.2    Larsson, S.3
  • 14
    • 0001164460 scopus 로고
    • A posteriori error bounds and global error control for approximation of ordinary differential equations
    • D. ESTEP, A posteriori error bounds and global error control for approximation of ordinary differential equations, SIAM J. Numer. Anal., 32 (1995), pp. 1-48.
    • (1995) SIAM J. Numer. Anal. , vol.32 , pp. 1-48
    • Estep, D.1
  • 17
    • 0345257516 scopus 로고
    • The h-, p- and hp-versions of the finite element method in one dimension, I: The error analysis of the p-version
    • W. GUI AND I. BABUŠKA, The h-, p- and hp-versions of the finite element method in one dimension, I: The error analysis of the p-version, Numer. Math., 49 (1986), pp. 577-612.
    • (1986) Numer. Math. , vol.49 , pp. 577-612
    • Gui, W.1    Babuška, I.2
  • 18
    • 34250122149 scopus 로고
    • The h-, p- and hp-versions of the finite element method in one dimension, II: The error analysis of the h- and hp-versions
    • W. GUI AND I. BABUŠKA, The h-, p- and hp-versions of the finite element method in one dimension, II: The error analysis of the h- and hp-versions, Numer. Math., 49 (1986), pp. 613-657.
    • (1986) Numer. Math. , vol.49 , pp. 613-657
    • Gui, W.1    Babuška, I.2
  • 19
    • 34250128680 scopus 로고
    • The h-, p- and hp-versions of the finite element method in one dimension, III: The adaptive hp-version
    • W. GUI AND I. BABUŠKA, The h-, p- and hp-versions of the finite element method in one dimension, III: The adaptive hp-version, Numer. Math., 49 (1986), pp. 659-683.
    • (1986) Numer. Math. , vol.49 , pp. 659-683
    • Gui, W.1    Babuška, I.2
  • 20
    • 0001394496 scopus 로고
    • Solving Ordinary Differential Equations, I: Non-stiff Problems
    • Springer-Verlag, Heidelberg
    • E. HAIRER, S.P. NØRSETT, AND G. WANNER, Solving Ordinary Differential Equations, I: Non-stiff Problems, Springer Ser. Comput. Math., 8, Springer-Verlag, Heidelberg, 1987.
    • (1987) Springer Ser. Comput. Math. , vol.8
    • Hairer, E.1    NØrsett, S.P.2    Wanner, G.3
  • 21
    • 0003312809 scopus 로고
    • Solving Ordinary Differential Equations, II: Stiff and Differential-Algebraic Problems
    • Springer-Verlag, Heidelberg
    • E. HAIRER AND G. WANNER, Solving Ordinary Differential Equations, II: Stiff and Differential-Algebraic Problems, Springer Ser. Comput. Math., 14, Springer-Verlag, Heidelberg, 1991.
    • (1991) Springer Ser. Comput. Math. , vol.14
    • Hairer, E.1    Wanner, G.2
  • 22
    • 0002298440 scopus 로고
    • Galerkin-type approximations which are discontinuous in time for parabolic equations in a variable domain
    • P. JAMET, Galerkin-type approximations which are discontinuous in time for parabolic equations in a variable domain, SIAM J. Numer. Anal., 15 (1978), pp. 912-928.
    • (1978) SIAM J. Numer. Anal. , vol.15 , pp. 912-928
    • Jamet, P.1
  • 23
    • 0001562231 scopus 로고
    • Error estimates and adaptive time-step control for a class of one-step methods for stiff ordinary differential equations
    • C. JOHNSON, Error estimates and adaptive time-step control for a class of one-step methods for stiff ordinary differential equations, SIAM J. Numer. Anal., 25 (1988), pp. 908-926.
    • (1988) SIAM J. Numer. Anal. , vol.25 , pp. 908-926
    • Johnson, C.1
  • 24
    • 0032355554 scopus 로고    scopus 로고
    • Numerical solution of parabolic integro-differential equations by the discontinuous Galerkin method
    • S. LARSSON, V. THOMÉE, AND L.B. WAHLBIN, Numerical solution of parabolic integro-differential equations by the discontinuous Galerkin method, Math. Comp., 67 (1998), pp. 45-71.
    • (1998) Math. Comp. , vol.67 , pp. 45-71
    • Larsson, S.1    Thomée, V.2    Wahlbin, L.B.3
  • 27
    • 0001503989 scopus 로고    scopus 로고
    • On the stability of the discontinuous Galerkin method for the heat equation
    • CH.G. MAKRIDAKIS AND I. BABUŠKA, On the stability of the discontinuous Galerkin method for the heat equation, SIAM J. Numer. Anal., 34 (1997), pp. 389-401.
    • (1997) SIAM J. Numer. Anal. , vol.34 , pp. 389-401
    • Makridakis, Ch.G.1    Babuška, I.2
  • 28
    • 0344307755 scopus 로고    scopus 로고
    • hp-FEM for reaction-diffusion equations, I: Robust exponential convergence
    • J.M. MELENK AND C. SCHWAB, hp-FEM for reaction-diffusion equations, I: Robust exponential convergence, SIAM J. Numer. Anal., 35 (1998), pp. 1520-1557.
    • (1998) SIAM J. Numer. Anal. , vol.35 , pp. 1520-1557
    • Melenk, J.M.1    Schwab, C.2
  • 29
    • 0032623107 scopus 로고    scopus 로고
    • Analytic regularity for a singularly perturbed problem
    • J.M. MELENK AND C. SCHWAB, Analytic regularity for a singularly perturbed problem, SIAM J. Math. Anal., 30 (1999), pp. 379-400.
    • (1999) SIAM J. Math. Anal. , vol.30 , pp. 379-400
    • Melenk, J.M.1    Schwab, C.2
  • 30
    • 0032209437 scopus 로고    scopus 로고
    • A discontinuous hp finite element method for diffusion problems
    • J.T. ODEN, I. BABUŠKA, AND C.E. BAUMANN, A discontinuous hp finite element method for diffusion problems, J. Comput. Phys., 146 (1998), pp. 495-519.
    • (1998) J. Comput. Phys. , vol.146 , pp. 495-519
    • Oden, J.T.1    Babuška, I.2    Baumann, C.E.3
  • 32
    • 0003748361 scopus 로고    scopus 로고
    • Projection and Quasi-Compressibility Methods for Solving the Incompressible Navier-Stokes Equations
    • Teubner, Stuttgart
    • A. PROHL, Projection and Quasi-Compressibility Methods for Solving the Incompressible Navier-Stokes Equations, Adv. Numer. Math., Teubner, Stuttgart, 1997.
    • (1997) Adv. Numer. Math.
    • Prohl, A.1
  • 35
    • 85046528180 scopus 로고    scopus 로고
    • An hp α-priori error analysis of the DG time-stepping method for initial value problems
    • to appear
    • D. SCHÖTZAU AND C. SCHWAB, An hp α-priori error analysis of the DG time-stepping method for initial value problems, Calcolo, to appear.
    • Calcolo
    • Schötzau, D.1    Schwab, C.2
  • 38
    • 0041622292 scopus 로고    scopus 로고
    • The p- and hp-versions of the finite element method for problems with boundary layers
    • C. SCHWAB AND M. SURI, The p- and hp-versions of the finite element method for problems with boundary layers, Math. Comp., 65 (1996), pp. 1403-1429.
    • (1996) Math. Comp. , vol.65 , pp. 1403-1429
    • Schwab, C.1    Suri, M.2
  • 39
    • 0032507570 scopus 로고    scopus 로고
    • The hp-version of the FEM for problems in mechanics with boundary layers
    • C. SCHWAB, M. SURI, AND C.A. XENOPHONTOS, The hp-version of the FEM for problems in mechanics with boundary layers, Comput. Methods Appl. Mech. Engrg., 157 (1998), pp. 311-333.
    • (1998) Comput. Methods Appl. Mech. Engrg. , vol.157 , pp. 311-333
    • Schwab, C.1    Suri, M.2    Xenophontos, C.A.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.