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 transi...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.展开更多
基金supported by NSFC grant 10971211,FANEDD,FANEDD of CAS and the Fundamental Research Funds for the Central UniversitiesAdditional support is provided by the Alexander von Humboldt-Foundation while the author was in residence at Freiburg University,Germanysupported by ARO grant W911NF-08-1-0520 and NSF grant DMS-0809086.
文摘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.
