报告人: 孟雄 哈尔滨工业大学

  

时间： 2018年6月29日 上午 10:30-11:30 

地点： 管理科研楼 1208

报告摘要：

In this talk, an analysis of the accuracy-enhancement for the discontinuous Galerkin (DG) method applied to one-dimensional scalarnonlinear hyperbolic conservation laws is carried out. This requires analyzing the divided difference of the errors for the DG solution. We therefore first prove that the $/alpha$-th order $(1 /le /alpha /le k+1)$ divided difference of the DG error in the$L^2$ norm is of order $k+3/2-/alpha/2$ when upwind fluxes are used, under the condition that$|/f'(u)$ possesses a uniform positive lower bound. By the duality argument,we then derive superconvergence results of order $2k+3/2-/alpha/2$ in the negative-order norm, demonstrating that it is possibleto extend the Smoothness-Increasing Accuracy-Conserving filter to nonlinear conservation laws to obtain at least$3k/2+1$th order superconvergence for post-processed solutions. As a by-product,for variable coefficient hyperbolic equations, we provide an explicit proof foroptimal convergence results of order $k+1$ in the $L^2$ norm for the divided differences of DG errors and thus $(2k+1)$th order superconvergence in negative-order norm holds. Numerical experiments are given that confirm the theoretical results.