报告题目：Structure-preserving arbitrary Lagrangian-Eulerian discontinuous Galerkin methods for hyperbolic conservation law with source term
报告人：徐岩
工作单位：中国科学技术大学
报告时间：2024年11月15日下午2:30-4:30.
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报告摘要：We develop the structure-preserving Lagrangian-Eulerian discontinuous Galerkin (ALE-DG) methods for a class of hyperbolic conservation laws with source term, which can preserve a general hydrostatic equilibrium state and positivity-preserving property under a suitable time step at the same time. Such equations mainly include the shallow water equations with non-flat bottom topography and the Euler equations with gravitation. By introducing well-balanced numerical fluxes and corresponding source term approximations, we established well-balanced schemes. We also discuss about the weak positivity property of the proposed schemes, and the positivity-preserving limiter can be applied to effectively enforce the positivity-preserving property. Numerical examples have been provided not only to demonstrate the good properties but also to show the advantages on moving mesh.
报告人简介：徐岩，中国科学技术大学教授、博士生导师。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、霍英东青年教师基础研究课题等科研项目，担任中国数学会计算数学分会理事，担任SlAM Journal on Scientific Computing, 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。
