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Volumn 31, Issue 1, 2008, Pages 584-607

Convergence of high order finite volume weighted essentially nonoscillatory scheme and discontinuous galerkin method for nonconvex conservation laws

Author keywords

Convergence; Discontinuous Galerkin method; Entropic projection; Entropy solution; Finite volume weighted essentially nonoscillatory scheme; Nonconvex conservation laws

Indexed keywords

ENTROPY; FINITE ELEMENT METHOD; PHYSICAL PROPERTIES;

EID: 77954197881     PISSN: 10648275     EISSN: 10957197     Source Type: Journal    
DOI: 10.1137/070687487     Document Type: Article
Times cited : (18)

References (20)
  • 1
    • 0030509253 scopus 로고    scopus 로고
    • A MUSCL method satisfying all the numerical entropy inequalities
    • F. Bouchut, C. H. Bourdarias, and B. Perthame, A MUSCL method satisfying all the numerical entropy inequalities, Math. Comp., 65 (1996), pp. 1438-1461.
    • (1996) Math. Comp. , vol.65 , pp. 1438-1461
    • Bouchut, F.1    Bourdarias, C.H.2    Perthame, B.3
  • 2
    • 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
  • 3
    • 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
  • 4
    • 84966217981 scopus 로고
    • Monotone difference approximations for scalar conservation laws
    • M. G. Crandall and A. Majda, Monotone difference approximations for scalar conservation laws, Math. Comp., 34 (1980), pp. 1-21.
    • (1980) Math. Comp. , vol.34 , pp. 1-21
    • Crandall, M.G.1    Majda, A.2
  • 5
    • 33645452809 scopus 로고    scopus 로고
    • Second-order entropy diminishing scheme for the Euler equations
    • F. Coquel, P. Helluy, and J. Schneider, Second-order entropy diminishing scheme for the Euler equations, Internat. J. Numer. Methods Fluids, 50 (2006), pp. 1029-1061.
    • (2006) Internat. J. Numer. Methods Fluids , vol.50 , pp. 1029-1061
    • Coquel, F.1    Helluy, P.2    Schneider, J.3
  • 6
    • 0030501943 scopus 로고    scopus 로고
    • An entropy satisfying MUSCL scheme for systems of conservation laws
    • F. Coquel and P. LeFloch, An entropy satisfying MUSCL scheme for systems of conservation laws, Numer. Math., 74 (1996), pp. 1-33.
    • (1996) Numer. Math. , vol.74 , pp. 1-33
    • Coquel, F.1    LeFloch, P.2
  • 7
    • 84968487025 scopus 로고
    • On cell entropy inequality for discontinuous Galerkin methods
    • G.-S. Jiang and C.-W. Shu, On cell entropy inequality for discontinuous Galerkin methods, Math. Comp., 62 (1994), pp. 531-538.
    • (1994) Math. Comp. , vol.62 , pp. 531-538
    • Jiang, G.-S.1    Shu, C.-W.2
  • 8
    • 0030161771 scopus 로고    scopus 로고
    • Efficient implementation of weighted ENO schemes
    • G.-S. Jiang and C.-W. Shu, Efficient implementation of weighted ENO schemes, J. Comput. Phys., 126 (1996), pp. 202-228.
    • (1996) J. Comput. Phys. , vol.126 , pp. 202-228
    • Jiang, G.-S.1    Shu, C.-W.2
  • 9
    • 0141976338 scopus 로고    scopus 로고
    • Weakly nonoscillatory schemes for scalar conservation laws
    • K. Kopotun, M. Neamtu, and B. Popov, Weakly nonoscillatory schemes for scalar conservation laws, Math. Comp., 72 (2003), pp. 1747-1767.
    • (2003) Math. Comp. , vol.72 , pp. 1747-1767
    • Kopotun, K.1    Neamtu, M.2    Popov, B.3
  • 11
    • 0000592595 scopus 로고
    • Weighted essentially non-oscillatory schemes
    • X.-D. Liu, S. Osher, and T. Chan, Weighted essentially non-oscillatory schemes, J. Comput. Phys., 115 (1994), pp. 200-212.
    • (1994) J. Comput. Phys. , vol.115 , pp. 200-212
    • Liu, X.-D.1    Osher, S.2    Chan, T.3
  • 12
    • 84966232121 scopus 로고
    • On the convergence of the difference approximations to scalar conservation laws
    • S. Osher and E. Tadmor, On the convergence of the difference approximations to scalar conservation laws, Math. Comp., 50 (1988), pp. 19-51.
    • (1988) Math. Comp. , vol.50 , pp. 19-51
    • Osher, S.1    Tadmor, E.2
  • 13
    • 55349130686 scopus 로고    scopus 로고
    • Convergence of Godunov-type schemes for scalar conservation laws under large time steps
    • J.-M. Qiu and C.-W. Shu, Convergence of Godunov-type schemes for scalar conservation laws under large time steps, SIAM J. Numer. Anal., 46 (2008), pp. 2211-2237.
    • (2008) SIAM J. Numer. Anal. , vol.46 , pp. 2211-2237
    • Qiu, J.-M.1    Shu, C.-W.2
  • 14
    • 19644381369 scopus 로고    scopus 로고
    • Runge-Kutta discontinuous Galerkin method using WENO limiters
    • J.-X. Qiu and C.-W. Shu, Runge-Kutta discontinuous Galerkin method using WENO limiters, SIAM J. Sci. Comput., 26 (2005), pp. 907-929.
    • (2005) SIAM J. Sci. Comput. , vol.26 , pp. 907-929
    • Qiu, J.-X.1    Shu, C.-W.2
  • 15
    • 0036151484 scopus 로고    scopus 로고
    • A technique of treating negative weights in WENO schemes
    • J. Shi, C. Hu, and C.-W. Shu, A technique of treating negative weights in WENO schemes, J. Comput. Phys., 175 (2002), pp. 108-127.
    • (2002) J. Comput. Phys. , vol.175 , pp. 108-127
    • Shi, J.1    Hu, C.2    Shu, C.-W.3
  • 16
    • 45449125925 scopus 로고
    • Efficient implementation of essentially non-oscillatory shock capturing schemes
    • C.-W. Shu and S. Osher, Efficient implementation of essentially non-oscillatory shock capturing schemes, J. Comput. Phys., 77 (1988), pp. 439-471.
    • (1988) J. Comput. Phys. , vol.77 , pp. 439-471
    • Shu, C.-W.1    Osher, S.2
  • 17
    • 2442433925 scopus 로고
    • Towards the ultimate conservative difference scheme V. A second order sequel to Godunov's method
    • B. van Leer, Towards the ultimate conservative difference scheme V. A second order sequel to Godunov's method, J. Comput. Phys., 32 (1979), pp. 101-136.
    • (1979) J. Comput. Phys. , vol.32 , pp. 101-136
    • Van Leer, B.1
  • 18
    • 33744949897 scopus 로고    scopus 로고
    • Anti-diffusive finite difference WENO methods for shallow water with transport of pollutant
    • Z. Xu and C.-W. Shu, Anti-diffusive finite difference WENO methods for shallow water with transport of pollutant, J. Comput. Math., 24 (2006), pp. 239-251.
    • (2006) J. Comput. Math. , vol.24 , pp. 239-251
    • Xu, Z.1    Shu, C.-W.2
  • 19
    • 0043235518 scopus 로고    scopus 로고
    • On wavewise entropy inequality for high-resolution schemes II: Fully discrete MUSCL schemes with exact evolution in small time
    • H. Yang, On wavewise entropy inequality for high-resolution schemes II: Fully discrete MUSCL schemes with exact evolution in small time, SIAM J. Numer. Anal., 36 (1998), pp. 1-31.
    • (1998) SIAM J. Numer. Anal. , vol.36 , pp. 1-31
    • Yang, H.1
  • 20
    • 24644449311 scopus 로고    scopus 로고
    • Convergence of Godunov type schemes
    • H. Yang, Convergence of Godunov type schemes, Appl. Math. Lett., 9 (1996), pp. 63-67.
    • (1996) Appl. Math. Lett. , vol.9 , pp. 63-67
    • Yang, H.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.