A numerical method for fractal conservation laws

Jerome Droniou (1)

1 I3M - Institut de Mathématiques et de Modélisation de Montpellier

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∞ ∩ BV that the approximate solutions converge in L∞ weak-∗ and in Lp strong for p < ∞, and we give numerical results showing the efficiency of the scheme and illustrating qualitative properties of the solution to the fractal conservation law.

Domaines: Equations aux dérivées partielles [math.AP]; Analyse numérique [math.NA]

Jerome Droniou. A numerical method for fractal conservation laws. Mathematics of Computation, 2010, 79 (269), pp.95-124. ⟨10.1090/S0025-5718-09-02293-5⟩. ⟨hal-00808696⟩