Volume 10, Issue 2
Local Discontinuous Galerkin Methods for the Degasperis-Procesi Equation

Yan Xu & Chi-Wang Shu

Commun. Comput. Phys., 10 (2011), pp. 474-508.

Published online: 2011-10

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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 L 2 stability for general solutions. The proof of the total variation stability of the schemes for the piecewise constant P 0 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.

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@Article{CiCP-10-474, author = {Yan Xu and Chi-Wang Shu}, title = {Local Discontinuous Galerkin Methods for the Degasperis-Procesi Equation}, journal = {Communications in Computational Physics}, year = {2011}, volume = {10}, number = {2}, pages = {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 L 2 stability for general solutions. The proof of the total variation stability of the schemes for the piecewise constant P 0 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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.300410.300710a}, url = {http://global-sci.org/intro/article_detail/cicp/7451.html} }
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