메뉴 건너뛰기




Volumn 39, Issue 4, 2002, Pages 1254-1268

Spectral vanishing viscosity method for nonlinear conservation laws

Author keywords

Conservation law; Spectral method; Vanishing viscosity

Indexed keywords


EID: 0035452997     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036142999362687     Document Type: Article
Times cited : (50)

References (34)
  • 1
    • 0001701116 scopus 로고
    • Spectral methods for discontinuous problems
    • Numerical Methods for Fluid Dynamics II, K. W. Morton and M. J. Baines, eds., Clarendon Press, Oxford
    • S. ABARBANEL, D. GOTTLIEB, AND E. TADMOR, Spectral methods for discontinuous problems, in Numerical Methods for Fluid Dynamics II, Proceedings of the 1985 Conference on Numerical Methods for Fluid Dynamics, K. W. Morton and M. J. Baines, eds., Clarendon Press, Oxford, 1986, pp. 129-153.
    • (1986) Proceedings of the 1985 Conference on Numerical Methods for Fluid Dynamics , pp. 129-153
    • Abarbanel, S.1    Gottlieb, D.2    Tadmor, E.3
  • 2
    • 0002238930 scopus 로고
    • The spectral viscosity method applied to simulation of waves in a stratified atmosphere
    • O. ANDREASSEN, I. LIE, AND C.E. WASBERG, The spectral viscosity method applied to simulation of waves in a stratified atmosphere, J. Comput. Phys., 110 (1994), pp. 257-273.
    • (1994) J. Comput. Phys. , vol.110 , pp. 257-273
    • Andreassen, O.1    Lie, I.2    Wasberg, C.E.3
  • 6
    • 84968504287 scopus 로고
    • Spectral viscosity approximations to multidimensional scalar conservation laws
    • G.-Q. CHEN, Q. DU, AND E. TADMOR, Spectral viscosity approximations to multidimensional scalar conservation laws, Math. Comp., 61 (1993), pp. 629-643.
    • (1993) Math. Comp. , vol.61 , pp. 629-643
    • Chen, G.-Q.1    Du, Q.2    Tadmor, E.3
  • 7
    • 0000994152 scopus 로고    scopus 로고
    • Detection of edges in spectral data
    • A. GELB AND E. TADMOR, Detection of edges in spectral data, Appl. Comp. Harmonic Anal., 7 (1999), pp. 101-135.
    • (1999) Appl. Comp. Harmonic Anal. , vol.7 , pp. 101-135
    • Gelb, A.1    Tadmor, E.2
  • 8
    • 0034190412 scopus 로고    scopus 로고
    • Enhanced spectral viscosity approximations for conservation laws
    • A. GELB AND E. TADMOR, Enhanced spectral viscosity approximations for conservation laws, Appl. Numer. Math., 33 (2000), pp. 3-21.
    • (2000) Appl. Numer. Math. , vol.33 , pp. 3-21
    • Gelb, A.1    Tadmor, E.2
  • 9
    • 0034431580 scopus 로고    scopus 로고
    • Detection of edges in spectral data II. Nonlinear enhancement
    • A. GELB AND E. TADMOR, Detection of edges in spectral data II. Nonlinear enhancement, SIAM J. Numer. Anal., 38 (2000), pp. 1389-1408.
    • (2000) SIAM J. Numer. Anal. , vol.38 , pp. 1389-1408
    • Gelb, A.1    Tadmor, E.2
  • 10
    • 0023330604 scopus 로고
    • Stability analysis of spectral methods for hyperbolic initial-boundary value systems
    • D. GOTTLIEB L. LUSTMAN, AND E. TADMOR, Stability analysis of spectral methods for hyperbolic initial-boundary value systems, SIAM J. Numer. Anal., 24 (1987), pp. 241-256.
    • (1987) SIAM J. Numer. Anal. , vol.24 , pp. 241-256
    • Gottlieb, D.1    Lustman, L.2    Tadmor, E.3
  • 12
    • 0031381548 scopus 로고    scopus 로고
    • On the Gibbs phenomenon and its resolution
    • D. GOTTLIEB AND C.-W. SHU, On the Gibbs phenomenon and its resolution, SIAM Rev., 39 (1998), pp. 644-668.
    • (1998) SIAM Rev. , vol.39 , pp. 644-668
    • Gottlieb, D.1    Shu, C.-W.2
  • 13
    • 0002201787 scopus 로고
    • On the Gibbs phenomenon I: Recovering exponential accuracy from the Fourier partial sum of a nonperiodic analytic function
    • D. GOTTLIEB, C.-W. SHU, A. SOLOMONOFF, AND H. VANDEVEN, On the Gibbs phenomenon I: Recovering exponential accuracy from the Fourier partial sum of a nonperiodic analytic function, J. Comput. Appl. Math., 43 (1992), pp. 81-92.
    • (1992) J. Comput. Appl. Math. , vol.43 , pp. 81-92
    • Gottlieb, D.1    Shu, C.-W.2    Solomonoff, A.3    Vandeven, H.4
  • 14
    • 0001694389 scopus 로고
    • Recovering pointwise values of discontinuous data within spectral accuracy
    • Progress and Supercomputing in Computational Fluid Dynamics, E. M. Murman and S. S. Abarbanel, eds., Birkhauser, Boston
    • D. GOTTLIEB AND E. TADMOR, Recovering pointwise values of discontinuous data within spectral accuracy, in Progress and Supercomputing in Computational Fluid Dynamics, Proceedings of a 1984 U.S.-Israel Workshop, Progr. Sci. Comput. 6, E. M. Murman and S. S. Abarbanel, eds., Birkhauser, Boston, 1985, pp. 357-375.
    • (1985) Proceedings of a 1984 U.S.-Israel Workshop, Progr. Sci. Comput. , vol.6 , pp. 357-375
    • Gottlieb, D.1    Tadmor, E.2
  • 16
    • 0033446249 scopus 로고    scopus 로고
    • Boundary layers in weak solutions to hyperbolic conservation laws
    • K. T. JOSEPH AND P. G. LEFLOCH, Boundary layers in weak solutions to hyperbolic conservation laws, Arch. Rational Mech. Anal., 147 (1999), pp. 47-88.
    • (1999) Arch. Rational Mech. Anal. , vol.147 , pp. 47-88
    • Joseph, K.T.1    LeFloch, P.G.2
  • 17
    • 0002160841 scopus 로고    scopus 로고
    • A spectral vanishing viscosity method for large eddy simulations
    • G.-S. KARAMANOS AND G. KARNIADAKIS, A spectral vanishing viscosity method for large eddy simulations, J. Comput. Phys., 163 (2000), pp. 22-50.
    • (2000) J. Comput. Phys. , vol.163 , pp. 22-50
    • Karamanos, G.-S.1    Karniadakis, G.2
  • 18
    • 0003212160 scopus 로고
    • Hyperbolic systems of conservation laws and the mathematical theory of shock waves
    • SIAM, Philadelphia
    • P. D. LAX, Hyperbolic Systems of Conservation Laws and the Mathematical Theory of Shock Waves, CBMS-NSF Regional Conf. Ser. Appl. Math. 11, SIAM, Philadelphia, 1972.
    • (1972) CBMS-NSF Regional Conf. Ser. Appl. Math. , vol.11
    • Lax, P.D.1
  • 19
    • 0042541963 scopus 로고    scopus 로고
    • On the multidomain spectral viscosity method in multidomain Chebyshev discretizations
    • A. V. Ilin and L. R. Scott, eds., Department of Mathematics, University of Houston, Houston, TX
    • I. LIE, On the multidomain spectral viscosity method in multidomain Chebyshev discretizations, in Proceedings of the Third International Conference on Spectral and High-Order Methods (ICOSAHOM '95), A. V. Ilin and L. R. Scott, eds., Department of Mathematics, University of Houston, Houston, TX, 1996, pp. 121-130.
    • (1996) Proceedings of the Third International Conference on Spectral and High-order Methods (ICOSAHOM '95) , pp. 121-130
    • Lie, I.1
  • 20
    • 0001531858 scopus 로고    scopus 로고
    • Chebyshev-Legendre spectral viscosity method for nonlinear conservation laws
    • H. MA, Chebyshev-Legendre spectral viscosity method for nonlinear conservation laws, SIAM J. Numer. Anal., 35 (1998), pp. 869-892.
    • (1998) SIAM J. Numer. Anal. , vol.35 , pp. 869-892
    • Ma, H.1
  • 21
    • 0348024370 scopus 로고    scopus 로고
    • Chebyshev-Legendre super spectral viscosity method for nonlinear conservation laws
    • H. MA, Chebyshev-Legendre super spectral viscosity method for nonlinear conservation laws, SIAM J. Numer. Anal., 35 (1998), pp. 893-908.
    • (1998) SIAM J. Numer. Anal. , vol.35 , pp. 893-908
    • Ma, H.1
  • 22
    • 0000961081 scopus 로고
    • Analysis of the spectral vanishing viscosity method for periodic conservation laws
    • Y. MADAY AND E. TADMOR, Analysis of the spectral vanishing viscosity method for periodic conservation laws, SIAM J. Numer. Anal., 26 (1989), pp. 854-870.
    • (1989) SIAM J. Numer. Anal. , vol.26 , pp. 854-870
    • Maday, Y.1    Tadmor, E.2
  • 23
    • 0027577995 scopus 로고
    • Legendre pseudospectral viscosity method for nonlinear conservation laws
    • Y. MADAY, S. M. OULD KABER, AND E. TADMOR, Legendre pseudospectral viscosity method for nonlinear conservation laws, SIAM J. Numer. Anal., 30 (1993), pp. 321-342.
    • (1993) SIAM J. Numer. Anal. , vol.30 , pp. 321-342
    • Maday, Y.1    Ould Kaber, S.M.2    Tadmor, E.3
  • 24
    • 84912983533 scopus 로고
    • The fourier method for nonsmooth initial data
    • A. MAJDA, J. MCDONOUGH, AND S. OSHER, The Fourier method for nonsmooth initial data Math. Comp., 30 (1978), pp. 1041-1081.
    • (1978) Math. Comp. , vol.30 , pp. 1041-1081
    • Majda, A.1    Mcdonough, J.2    Osher, S.3
  • 25
    • 0030268701 scopus 로고    scopus 로고
    • A Legendre pseudospectral viscosity method
    • S. M. OULD KABER, A Legendre pseudospectral viscosity method, J. Comp. Phys., 128 (1996), pp. 165-180.
    • (1996) J. Comp. Phys. , vol.128 , pp. 165-180
    • Ould Kaber, S.M.1
  • 26
    • 0025502815 scopus 로고
    • The rate of convergence of spectral-viscosity methods for periodic scalar conservation laws
    • S. SCHOCHET, The rate of convergence of spectral-viscosity methods for periodic scalar conservation laws, SIAM J. Numer. Anal., 27 (1990), pp. 1142-1159.
    • (1990) SIAM J. Numer. Anal. , vol.27 , pp. 1142-1159
    • Schochet, S.1
  • 27
    • 0029370106 scopus 로고
    • A note on the accuracy of spectral method applied to nonlinear conservation laws
    • C. W. SHU AND P. WONG, A note on the accuracy of spectral method applied to nonlinear conservation laws, J. Sci. Comput., 10 (1995), pp. 357-369.
    • (1995) J. Sci. Comput. , vol.10 , pp. 357-369
    • Shu, C.W.1    Wong, P.2
  • 29
    • 0002147664 scopus 로고
    • Convergence of spectral methods for nonlinear conservation laws
    • E. TADMOR, Convergence of spectral methods for nonlinear conservation laws, SIAM J. Numer. Anal., 26 (1989), pp. 30-44.
    • (1989) SIAM J. Numer. Anal. , vol.26 , pp. 30-44
    • Tadmor, E.1
  • 30
    • 0025448705 scopus 로고
    • Shock capturing by the spectral viscosity method
    • E. TADMOR, Shock capturing by the spectral viscosity method, Comput. Methods Appl. Mech. Engrg., 80 (1990), pp. 197-208.
    • (1990) Comput. Methods Appl. Mech. Engrg. , vol.80 , pp. 197-208
    • Tadmor, E.1
  • 31
    • 0026203648 scopus 로고
    • Local error estimates for discontinuous solutions of nonlinear hyperbolic equations
    • E. TADMOR, Local error estimates for discontinuous solutions of nonlinear hyperbolic equations, SIAM J. Numer. Anal., 28 (1991), pp. 891-906.
    • (1991) SIAM J. Numer. Anal. , vol.28 , pp. 891-906
    • Tadmor, E.1
  • 32
    • 84968499102 scopus 로고
    • Total-variation and error estimates for spectral viscosity approximations
    • E. TADMOR, Total-variation and error estimates for spectral viscosity approximations Math Comp., 60 (1993), pp. 245-256.
    • (1993) Math Comp. , vol.60 , pp. 245-256
    • Tadmor, E.1
  • 33
    • 0002065170 scopus 로고
    • Super viscosity and spectral approximations on nonlinear conservation laws
    • Numerical Methods for Fluid Dynamics IV, M. J. Baines and K. W. Morton, eds., Clarendon Press, Oxford
    • E. TADMOR, Super viscosity and spectral approximations on nonlinear conservation laws, in Numerical Methods for Fluid Dynamics IV, Proceedings of the 1992 Conference on Numerical Methods for Fluid Dynamics, M. J. Baines and K. W. Morton, eds., Clarendon Press, Oxford, 1993, pp. 69-82.
    • (1993) Proceedings of the 1992 Conference on Numerical Methods for Fluid Dynamics , pp. 69-82
    • Tadmor, E.1
  • 34
    • 0000440966 scopus 로고
    • Compensated compactness and applications to partial differential equations
    • J. Knopps, ed., Pitman, Boston, London
    • L. TARTAR, Compensated compactness and applications to partial differential equations, in Nonlinear Analysis and Mechanics: Heriot-Watt Symposium, Vol. IV, Res. Notes in Math. 39, J. Knopps, ed., Pitman, Boston, London, 1979, pp. 136-212.
    • (1979) Nonlinear Analysis and Mechanics: Heriot-Watt Symposium, Vol. IV, Res. Notes in Math. , vol.39 , pp. 136-212
    • Tartar, L.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.