报告题目：Discontinuous Galerkin methods with generalized numerical fluxes for several time dependent convection-dominated PDEs
报告人：孟雄 哈尔滨工业大学
报告时间：4月29日（周一）13:00-14:00
报告地点：教2-314
主办单位：南京邮电大学理学院
邀请人：王海金
报告内容：In this talk, we first consider the discontinuous Galerkin method using generalized numerical fluxes for linearized KdV equations. We are able to choose a downwind-biased flux in possession of the anti-dissipation property for the convection term to compensate the numerical dissipation of the dispersion term. This is beneficial to obtain a lower growth of the error and to accurately capture the exact solution without phase errors for long time simulations. By establishing relationships of different numerical viscosity coefficients, a uniform stability is shown. Moreover, a suitable numerical initial condition is chosen. By using generalized Gauss-Radau projections, optimal error estimates are derived. Extensions of discontinuous Galerkin methods with generalized fluxes for nonlinear convection-diffusion systems, nonlinear Schrödinger equations and nonlinear hyperbolic conservation laws are also given. Numerical experiments are provided to confirm the theoretical results.
报告人简介：孟雄，哈尔滨工业大学数学学院教授、博导、省优青，欧盟玛丽居里学者、美国布朗大学访问学者，主要研究方向为计算流体力学间断有限元方法的设计、分析与应用。在SIAM Journal on Numerical Analysis, Numerische Mathematik, Mathematics of Computation等期刊发表论文17篇。主持欧盟“玛丽居里行动”计划基金、国家自然科学基金面上项目、国家自然科学基金青年基金等项目。获中国工业与应用数学学会应用数学青年科技奖和国家天元数学东北中心优秀青年学者等奖励。