The discontinuous Galerkin method for fractional degenerate convection-diffusion equationsReport as inadecuate

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BIT Numerical Mathematics

, Volume 51, Issue 4, pp 809–844

First Online: 29 March 2011Received: 12 March 2010Accepted: 09 March 2011


We propose and study discontinuous Galerkin methods for strongly degenerate convection-diffusion equations perturbed by a fractional diffusion Lévy operator. We prove various stability estimates along with convergence results toward properly defined entropy solutions of linear and nonlinear equations. Finally, the qualitative behavior of solutions of such equations are illustrated through numerical experiments.

KeywordsConvection-diffusion equations Degenerate parabolic Conservation laws Fractional diffusion Entropy solutions Direct-local discontinuous Galerkin methods Communicated by Ralf Hiptmair.

This research was supported by the Research Council of Norway NFR through the project -Integro-PDEs: Numerical methods, Analysis, and Applications to Finance-. This article was written as part of the international research program on Nonlinear Partial Differential Equations at the Centre for Advanced Study at the Norwegian Academy of Science and Letters in Oslo during the academic year 2008–09.

Mathematics Subject Classification 200065M60 65M12 35K59 35R11 35K65 35L67  Download to read the full article text

Author: Simone Cifani - Espen R. Jakobsen - Kenneth H. Karlsen


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