Local Discontinuous Galerkin Methods for the Degasperis-Procesi Equation (Communications in Computational Physics, 2011)
In this paper, we develop, analyze and test local discontinuous Galerkin(LDG) methods for solving the Degasperis-Procesi equation which contains nonlinearhigh order derivatives, and possibly discontinuous or sharp transition solutions. TheLDG method has the flexibility for arbitrary h and p adaptivity. We prove the L2 stabilityfor general solutions. The proof of the total variation stability of the schemesfor the piecewise constant P0 case is also given. The numerical simulation results fordifferent types of solutions of the nonlinear Degasperis-Procesi equation are providedto illustrate the accuracy and capability of the LDG method.