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

Yan Xu & Chi-Wang Shu

DOI: 10.4208/cicp.300410.300710a

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 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.

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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 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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.300410.300710a}, url = {http://global-sci.org/intro/article_detail/cicp/7451.html} }
TY - JOUR T1 - Local Discontinuous Galerkin Methods for the Degasperis-Procesi Equation AU - Yan Xu & Chi-Wang Shu JO - Communications in Computational Physics VL - 2 SP - 474 EP - 508 PY - 2011 DA - 2011/10 SN - 10 DO - http://doi.org/10.4208/cicp.300410.300710a UR - https://global-sci.org/intro/article_detail/cicp/7451.html KW - AB -

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.

Yan Xu and Chi-Wang Shu. (2011). Local Discontinuous Galerkin Methods for the Degasperis-Procesi Equation. Communications in Computational Physics. 10 (2). 474-508. doi:10.4208/cicp.300410.300710a
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