Local Discontinuous Galerkin Methods for the Degasperis-Procesi Equation

Local Discontinuous Galerkin Methods for the Degasperis-Procesi Equation

Year:    2011

Communications in Computational Physics, Vol. 10 (2011), Iss. 2 : pp. 474–508

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 Lstability for general solutions. The proof of the total variation stability of the schemes for the piecewise constant Pcase 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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/cicp.300410.300710a

Communications in Computational Physics, Vol. 10 (2011), Iss. 2 : pp. 474–508

Published online:    2011-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    35

Keywords:   

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