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Volumn 22, Issue 1, 2005, Pages 79-99

Local error analysis for approximate solutions of hyperbolic conservation laws

Author keywords

Conservation laws; Error estimates; Truncation error; Weak solutions

Indexed keywords


EID: 14544284969     PISSN: 10197168     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10444-005-7099-8     Document Type: Article
Times cited : (34)

References (19)
  • 1
    • 0040456047 scopus 로고    scopus 로고
    • Advanced Numerical Approximation of Nonlinear Hyperbolic Equations
    • C.I.M.E. Course in Cetraro, Italy, June, ed. A. Quarteroni, Springer, New York
    • B. Cockburn, C. Johnson, C.-W. Shu and E. Tadmor, Advanced Numerical Approximation of Nonlinear Hyperbolic Equations, C.I.M.E. Course in Cetraro, Italy, June 1997, ed. A. Quarteroni, Lecture Notes in Mathematics, Vol. 1697 (Springer, New York, 1998).
    • (1997) Lecture Notes in Mathematics , vol.1697
    • Cockburn, B.1    Johnson, C.2    Shu, C.-W.3    Tadmor, E.4
  • 2
    • 0003363041 scopus 로고
    • A Practical Guide to Splines
    • Springer, New York
    • C. de Boor, A Practical Guide to Splines, Applied Mathematical Sciences, Vol. 27 (Springer, New York, 1978).
    • (1978) Applied Mathematical Sciences , vol.27
    • De Boor, C.1
  • 5
    • 0037141034 scopus 로고    scopus 로고
    • A smoothness indicator for adaptive algorithms for hyperbolic systems
    • S. Karni, A. Kurganov and G. Petrova, A smoothness indicator for adaptive algorithms for hyperbolic systems, J. Comput. Phys. 178 (2002) 323-341.
    • (2002) J. Comput. Phys. , vol.178 , pp. 323-341
    • Karni, S.1    Kurganov, A.2    Petrova, G.3
  • 8
    • 0036288577 scopus 로고    scopus 로고
    • Semi-discrete central-upwind scheme for hyperbolic conservation laws and Hamilton-Jacobi equations
    • A. Kurganov, S. Noelle and G. Petrova, Semi-discrete central-upwind scheme for hyperbolic conservation laws and Hamilton-Jacobi equations, SIAM J. Sci. Comput. 23 (2001) 707-740.
    • (2001) SIAM J. Sci. Comput. , vol.23 , pp. 707-740
    • Kurganov, A.1    Noelle, S.2    Petrova, G.3
  • 9
    • 0003733595 scopus 로고    scopus 로고
    • Finite Volume Methods for Hyperbolic Problems
    • Cambridge Univ. Press, Cambridge
    • R. LeVeque, Finite Volume Methods for Hyperbolic Problems, Cambridge Texts in Applied Mathematics (Cambridge Univ. Press, Cambridge, 2002).
    • (2002) Cambridge Texts in Applied Mathematics
    • LeVeque, R.1
  • 10
    • 0026972508 scopus 로고
    • The convergence rate of approximate solutions for nonlinear scalar conservation laws
    • H. Nessyahu and E. Tadmor, The convergence rate of approximate solutions for nonlinear scalar conservation laws, SIAM J. Numer. Anal. 29 (1992) 1505-1519.
    • (1992) SIAM J. Numer. Anal. , vol.29 , pp. 1505-1519
    • Nessyahu, H.1    Tadmor, E.2
  • 11
  • 13
    • 2942757053 scopus 로고
    • Approximate Riemann solvers, parameter vectors and difference schemes
    • P. L. Roe, Approximate Riemann solvers, parameter vectors and difference schemes, J. Comput. Phys. 43 (1981) 357-372.
    • (1981) J. Comput. Phys. , vol.43 , pp. 357-372
    • Roe, P.L.1
  • 15
    • 2942705023 scopus 로고
    • A survey of several finite difference methods for systems of nonlinear hyperbolic conservation laws
    • G. Sod, A survey of several finite difference methods for systems of nonlinear hyperbolic conservation laws, J. Comput. Phys. 22 (1978) 1-31.
    • (1978) J. Comput. Phys. , vol.22 , pp. 1-31
    • Sod, G.1
  • 16
    • 14544276775 scopus 로고    scopus 로고
    • A posteriori error analysis and adaptivity for finite element approximations of hyperbolic problems
    • eds. D. Kröner, M. Ohlberger and C. Rhode, Springer, New York, also, Technical Report NA-97/21, Oxford University Computing Laboratory
    • E. Süli, A posteriori error analysis and adaptivity for finite element approximations of hyperbolic problems, Lecture Notes in Computer Science and Engineering, eds. D. Kröner, M. Ohlberger and C. Rhode, Vol. 5 (Springer, New York, 1998); also, Technical Report NA-97/21, Oxford University Computing Laboratory (1997); http://web.comlab.ox.ac.uk/oucl/publications/natr/ na-97-21.html.
    • (1997) Lecture Notes in Computer Science and Engineering , vol.5
    • Süli, E.1
  • 17
    • 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) 891-906.
    • (1991) SIAM J. Numer. Anal. , vol.28 , pp. 891-906
    • Tadmor, E.1
  • 18
    • 0007281577 scopus 로고    scopus 로고
    • Pointwise convergence rate for nonlinear conservation laws
    • Zürich, eds. M. Fey and R. Jeltsch, International Series of Numerical Mathematics, Birkhäuser, Basel
    • E. Tadmor and T. Tang, Pointwise convergence rate for nonlinear conservation laws, in: Proc. of the 7th Internat. Conf. on Hyperbolic Problems, Zürich, 1998, eds. M. Fey and R. Jeltsch, International Series of Numerical Mathematics, Vol. 130 (Birkhäuser, Basel, 1999) pp. 925-934.
    • (1998) Proc. of the 7th Internat. Conf. on Hyperbolic Problems , vol.130 , pp. 925-934
    • Tadmor, E.1    Tang, T.2
  • 19
    • 0001176128 scopus 로고    scopus 로고
    • Pointwise error estimates for scalar conservation laws with piecewise smooth solutions
    • E. Tadmor and T. Tang, Pointwise error estimates for scalar conservation laws with piecewise smooth solutions, SIAM J. Numer. Anal. 36 (1999) 1739-1756.
    • (1999) SIAM J. Numer. Anal. , vol.36 , pp. 1739-1756
    • Tadmor, E.1    Tang, T.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.