On Large Time Step Godunov Scheme for Hyperbolic Conservation Laws
نویسندگان
چکیده
In this paper we study the large time step (LTS) Godunov scheme proposed by LeVeque for nonlinear hyperbolic conservation laws. As we known, when the Courant number is larger than 1, the linear interactions of the elementary waves in this scheme will be much more complicated than those for Courant number less than 1. In this paper, we will show that for scalar conservation laws, for any fixed Courant number, all the possible wave interactions in each time step tj < t < tj+1 only happen in finite number of cells, and the number is bounded by a constant depending only on the Courant number for a given initial value problem if the initial data is BV . This implies that the total length of the linear superposition zone in x direction will go to zero as the spatial step size goes to 0. And as an application of the result mentioned above, we show that for any given Courant number, if the total variation of the initial data satisfies some conditions, the solutions of the LTS Godunov scheme will converge to the entropy solutions for the convex scalar conservation laws.
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