题  目：Energy conserving discontinuous Galerkin methods for the wave equations

报告人: Dr. Yulong Xing  
       University of Tennessee

时  间： 2011年12月29日 16:30

地  点： 管理科研楼 1518

摘  要:
In this presentation, we construct, analyze, and numerically validate a class of energy conserving discontinuous Galerkin schemes for the wave equations. In the first part of the talk, we consider the Korteweg-de Vries (KdV) equation, which is a nonlinear mathematical model for the unidirectional propagation of waves in a variety of nonlinear, dispersive media. Conservative discontinuous Galerkin schemes are developed for the generalized KdV equation. The schemes preserve the first two invariants (the integral and L2 norm) of the numerical approximations. We provide numerical evidence that this property imparts the approximations with beneficial attributes such as more faithful reproduction of the amplitude and phase of traveling wave solutions.

In the second part, we consider the linear wave equation, and develop the local discontinuous Galerkin method for solving it. We prove the optimal error estimates, superconvergence toward a particular projection of the exact solution, and the energy conserving property for the semi-discrete formulation. Numerical experiments have been provided to demonstrate the optimal rates of convergence and superconvergence.

主办单位： 中国科学技术大学数学科学学院     
          国家数学与交叉科学中心合肥分中心
          中国科学技术大学研究生院

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