A numerical method for fractal conservation laws

Droniou, Jérôme

doi:10.1090/S0025-5718-09-02293-5

A numerical method for fractal conservation laws
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Math. Comp. 79 (2010), 95-124 Request permission

Abstract:

We consider a fractal scalar conservation law, that is to say, a conservation law modified by a fractional power of the Laplace operator, and we propose a numerical method to approximate its solutions. We make a theoretical study of the method, proving in the case of an initial data belonging to $L^\infty \cap BV$ that the approximate solutions converge in $L^\infty$ weak-$*$ and in $L^p$ strong for $p<\infty$, and we give numerical results showing the efficiency of the scheme and illustrating qualitative properties of the solution to the fractal conservation law.

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