题目：Well-balanced arbitrary Lagrangian-Eulerian discontinuous Galerkin methods for the shallow water equations
报告人：徐岩教授（中国科学技术大学）
报告时间：2020年9月 4日上午10:00-11:30
腾讯会议ID: 370 522 386
摘要: In this paper, we develop well-balanced arbitrary Lagrangian-Eulerian discontinuous Galerkin (ALE-DG) methods for the shallow water equations, which preserve not only the still water equilibrium, but also the moving water equilibrium. Based on the time dependent linear affine mapping, the ALE-DG method for conservation laws maintains almost all mathematical properties of DG methods on static grids, such as conservation, geometric conservation law (GCL), entropy stability and optimal error estimates. The main difficulty to obtain the well-balanced property of the ALE-DG method for shallow water equations is that the grid movement and usual time discretization may destroy the equilibrium. By adopting the GCL preserving Runge-Kutta methods and the techniques of well-balanced DG schemes on static grids, we successfully construct the high order well-balanced ALE-DG schemes for the shallow water equations. Numerical experiments in different circumstances are provided to illustrate the well-balanced property and accuracy of these schemes.
报告人简介：徐岩，中国科学技术大学数学科学学院教授。2005年于中国科学技术大学数学系获计算数学博士学位。2005-2007年在荷兰Twente大学从事博士后研究工作。2009年获得德国洪堡基金会的支持在德国Freiburg大学访问工作一年。主要研究领域为高精度数值计算方法。2008年度获全国优秀博士学位论文奖，2017年获国家自然科学基金委“优秀青年基金”。徐岩教授入选了教育部新世纪优秀人才计划，主持国家自然科学基金面上项目、德国洪堡基金会研究组合作计划(Research Group Linkage Programme)、霍英东青年教师基础研究课题等科研项目。担任Journal of Scientific Computing, Advances in Applied Mathematics and Mechanics, Communication on Applied Mathematics and Computation、计算物理等杂志的编委。
