论文信息 - The Optimal Convergence Rate of Monotone Finite Difference Methods for Hyperbolic Conservation Laws

The Optimal Convergence Rate of Monotone Finite Difference Methods for Hyperbolic Conservation Laws

We are interested in the rate of convergence in L1 of the approximate solution of a conservation law generated by a monotone finite difference scheme. Kuznetsov has proved that this rate is 1/2 [USSR Comput. Math. Math. Phys., 16 (1976), pp. 105--119 and Topics Numer. Anal. III, in Proc. Roy. Irish Acad. Conf., Dublin, 1976, pp. 183--197], and recently Teng and Zhang have proved this estimate to be sharp for a linear flux [SIAM J. Numer. Anal., 34 (1997), pp. 959--978]. We prove, by constructing appropriate initial data for the Cauchy problem, that Kuznetsov's estimates are sharp for a nonlinear flux as well.

Florin Sabac | Florin Sabac | Florin Şabac

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