报告主题：波动方程的Galerkin方法
报告人：Chi-Wang Shu 教授 （美国布朗大学）
报告时间：2018年12月20日（周四）14：30
报告地点：校本部G507
邀请人：马和平
报告摘要：Energy conservation is an important property for many time dependent PDEs, such as linear hyperbolic systems, linear and nonlinear dispersive wave equations including KdV equations, etc. Discontinuous Galerkin (DG) methods are often used to solve such problems, especially when adaptivity is desired. However, it is difficult to design energy conserving DG methods for such problems with optimal convergence in the L^2-norm. In this talk we will describe our recent work in designing such DG schemes, which involves the technique of possible doubling of unknowns. Optimal a priori error estimates of order k+1 are obtained for the semi-discrete scheme in one dimension, and in multi-dimensions on Cartesian meshes when tensor-product polynomials of degree k are used, for linear hyperbolic and dispersive wave equations. Computational results for linear and nonlinear problems including those in aeroacoustics, Maxwell equations and KdV equations, on both structured and unstructured meshes, demonstrate the excellent performance of these energy conserving schemes. This is joint work with Guosheng Fu.
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