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1 results

  • Local Discontinuous Galerkin Methods for the Degasperis-Procesi Equation

  • Yan Xu, Chi-Wang Shu
  • Journal:
    Communications in Computational Physics / Volume 10 / Issue 2 / August 2011
    Published online by Cambridge University Press:
    20 August 2015, pp. 474-508
    Print publication:
    August 2011

  • 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.