The discontinuous Galerkin method for fractal conservation laws

We propose, analyze, and demonstrate a discontinuous Galerkin method for fractal conservation laws. Various stability estimates are established along with error estimates for regular solutions of linear equations. Moreover, in the nonlinear case and whenever piecewise constant elements are utilized,...

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Bibliographic Details
Published in:arXiv.org 2010-06
Main Authors: Cifani, Simone, Jakobsen, Espen R, Karlsen, Kenneth H
Format: Article
Language:English
Subjects:
Conservation laws
Entropy of solution
Fractal analysis
Fractals
Galerkin method
Linear equations
Nonlinear equations
Online Access:Get full text
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Summary:We propose, analyze, and demonstrate a discontinuous Galerkin method for fractal conservation laws. Various stability estimates are established along with error estimates for regular solutions of linear equations. Moreover, in the nonlinear case and whenever piecewise constant elements are utilized, we prove a rate of convergence toward the unique entropy solution. We present numerical results for different types of solutions of linear and nonlinear fractal conservation laws.
ISSN:2331-8422
DOI:10.48550/arxiv.0906.1092