报告人：陶琪教授（北京工业大学）

报告题目：An oscillation-free discontinuous Galerkin (OFDG) method for shallow water equations

报告摘要：(1) In this talk, we develop an oscillation-free discontinuous Galerkin (OFDG) method for solving the shallow water equations with a non-flat bottom topography. Due to the nonlinear hyperbolic nature of the shallow water equation, the exact solution may contain shock discontinuities; thus, the numerical solution may generate spurious oscillations if no special treatment is taken near the discontinuities. Besides, it is desirable to construct a numerical scheme that possesses the well-balanced property, which preserves exactly the hydrostatic equilibrium solutions up to the machine error.

(2) Moreover, based on the existing well-balanced DG schemes, we add an extra damping term to control the spurious oscillations. With the careful construction of the damping term, the proposed method not only achieves non-oscillatory property without compromising any order of accuracy, but also inherits the well-balanced property from original schemes. Extensive numerical experiments, including one- and two-dimensional space, demonstrate that the proposed method has desired properties without sacrificing any order of accuracy.

报告时间：2024年8月5日14:00-17:00

报告地点：理学楼501室

报告人简介：陶琪，北京工业大学理学部教授。于2020年获得中国科学技术大学博士学位。2018年至2020年在美国布朗大学应用数学系联合培养。2020年至2022年在北京计算科学研究中心做博士后。2022年加入北京工业大学，入选北京工业大学高层次人才计划。主要研究领域为间断有限元方法的理论分析及应用。在SIAM J. Numer. Anal., Math. Comp., J. Sci. Comput. 等国际期刊发表学术论文十余篇。曾获中国博士后基金特别资助和面上资助，现主持国家自然科学基金青年项目。