@Article{CiCP-10-474, author = {}, 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 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.

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