A numerical method for fractal conservation laws

: 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. Mathematics Subject Classification: 65M12, 35L65, 35S10, 45K05.

• Type: Journal
• Year: 2010
• Where: MOC
• Authors: Jérôme Droniou
• Keywords: Conservation Law, Fractal Conservation Law, Fractal Scalar Conservation, MOC 2010, Security Privacy