Mathematics of Computation

Author(s): Jérôme Droniou.
Journal: Math. Comp. 79 (2010), 95-124.
MSC (2000): Primary 65M12, 35L65, 35S10, 45K05
Posted: July 29, 2009
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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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Retrieve articles in Mathematics of Computation with MSC (2000): 65M12, 35L65, 35S10, 45K05

Jérôme Droniou
Affiliation: Université Montpellier 2, Institut de Mathématiques et de Modélisation de Montpellier, CC 051, Place Eugène Bataillon, 34095 Montpellier cedex 5, France
Email: droniou@math.univ-montp2.fr

DOI: 10.1090/S0025-5718-09-02293-5
PII: S 0025-5718(09)02293-5
Keywords: Conservation laws, L\'evy operator, fractal operator, integral operator, numerical scheme, proof of convergence, numerical results.
Received by editor(s): April 25, 2009
Received by editor(s) in revised form: March 23, 2009
Posted: July 29, 2009
Copyright of article: Copyright 2009, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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