Adaptive Solution of One{dimensional Scalar Conservation Laws with Convex Flux
نویسنده
چکیده
A new adaptive approach for one{dimensional scalar conservation laws with convex ux is proposed. The initial data are approximated on an adaptive grid by a problem dependent, monotone interpolation procedure in such a way, that the multivalued problem of characteristic transport can be easily and explicitly solved. The unique entropy solution is chosen by means of a selection criterion due to Hopf and Lax. For arbitrary times, the solution is represented by an adaptive monotone spline interpolation. The spatial approximation is controlled by local L 1 {error estimates. As a distinctive feature of the approach, there is no discretization in time. The method is monotone on xed grids. Numerical examples are included, to demonstrate the predicted behavior.
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تاریخ انتشار 1992