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Local Discontinuous Galerkin Methods for the Degasperis-Procesi Equation

Published online by Cambridge University Press:  20 August 2015

Yan Xu  and
Chi-Wang Shu
Yan Xu*
Affiliation:
Department of Mathematics, University of Science and Technology of China, Hefei 230026, Anhui, China
Chi-Wang Shu*
Affiliation:
Division of Applied Mathematics, Brown University, Providence, RI 02912, USA
*
Corresponding author.Email:yxu@ustc.edu.cn
Email:shu@dam.brown.edu
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Abstract

In this paper, we develop, analyze and test local discontinuous Galerkin (LDG) methods for solving the Degasperis-Procesi equation which contains nonlinear high order derivatives, and possibly discontinuous or sharp transition solutions. The LDG method has the flexibility for arbitrary h and p adaptivity. We prove the L2 stability for general solutions. The proof of the total variation stability of the schemes for the piecewise constant P0 case is also given. The numerical simulation results for different types of solutions of the nonlinear Degasperis-Procesi equation are provided to illustrate the accuracy and capability of the LDG method.

Keywords

65M6035Q53Local discontinuous Galerkin methodDegasperis-Procesi equationL2 stabilitytotal variation stability
Type
Research Article
Information
Communications in Computational Physics , Volume 10 , Issue 2 , August 2011 , pp. 474 - 508
Copyright
Copyright © Global Science Press Limited 2011

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