Mathematics of Computation

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ISSN 1088-6842(e) ISSN 0025-5718(p)

A numerical method for fractal conservation laws

Author(s): Jérôme Droniou.
Journal: Math. Comp. 79 (2010), 95-124.
MSC (2000): Primary 65M12, 35L65, 35S10, 45K05
Posted: July 29, 2009
MathSciNet review: 2552219
Retrieve article in: PDF

Abstract | References | Similar articles | Additional information

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 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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