报告题目：Structure preserving arbitrary Lagrangian-Eulerian discontinuous Galerkin methods for conservation laws and applications

报 告 人： 夏银华副教授  中国科学技术大学
　　报告时间： 2023年8月7日（星期一）上午10:30

报告地点： 文理楼290

报告人简介：

夏银华，中国科学技术大学数学学院副教授、博士生导师。中国科学技术大学数学系获得博士学位，先后到美国布朗大学、香港大学、德国维堡大学等从事博士后研究和访问工作。主要从事高精度数值方法和大规模科学计算的研究，应用于计算流体、天体物理、相场和交通流等方面的数值模拟，相关工作发表于Math. Comp., J. Comput. Phys., J. Sci. Comput., SIAM J. Num. Anal., SIAM J. Sci. Comput. 等杂志。近年来主持国家自然科学基金、教育部等多相科学基金项目的研究。担任美国数学会MathReview、德国数学文摘zbMATH评论员。

报告摘要：

In this talk, we present the arbitrary Lagrangian-Eulerian discontinuous Galerkin (ALE-DG) methods for conservation laws. The method will be designed for simplex meshes. This will ensure that the method satisfies the geometric conservation law for any time integration method with the accuracy order at least the same as the spatial dimension. For the semi-discrete method the L2-stability and the suboptimal (k + 1/2 ) convergence with respect to the L∞ (0, T ; L2 (Ω))-norm will be proven, when an arbitrary monotone flux is used and for each cell the approximating functions are given by polynomials of degree k. The two-dimensional fully-discrete explicit method will be combined with the bound preserving limiter. This limiter does not affect the high order accuracy of the numerical method. Then, for the ALE-DG method revised by the limiter the validity of a discrete maximum principle will be proven. This approach can also be developed for the positivity preserving of ALE-DG methods for Euler equations and the well-balanced ALE-DG method for shallow water equations. The numerical stability, robustness, and accuracy of the method will be shown by a variety of computational experiments on moving meshes.