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佘邦伟: On the convergence of numerical solutions for the compressible Navier-Stokes system

时间:2021-10-20来源:数学学院

报告时间:2021年10月21日(星期四)8:30-9:30

报告地点:翡翠湖校区科教楼B座1710会议室

佘邦伟 副研究员

工作单位首都师范大学

举办单位:数学学院

报告简介

We study the convergence of numerical solutions for the compressible Navier Stokes system in the sense of a generalized Lax equivalence theorem: convergence = stability + consistency. First, we define a consistent approximation representing the stability and consistency of a numerical sequence and show that the sequence converges towards a dissipative weak solution of the Navier-Stokes system. Then, by the weak-strong uniqueness principle, we conclude the convergence of the consistent approximation towards a strong solution as long as the latter exists. Further, we present numerical schemes whose solution fall into the class of the consistent approximation, which completes the whole convergence theory and indicates the global-in-time exisitence of a dissipative weak solution. Finally, we present a few numerical experiments to support the convergence theory.

报告人简介

佘邦伟,首都师范大学交叉科学研究院副研究员。曾任捷克科学院数学研究所研究员,查理大学数理学院数学分析专业兼职科研人员,研究领域为流体力学方程组的数值模拟和分析,在 Journal of Computational Physics, IMA Journal of Numerical Analysis, Multiscale Modeling and Simulation, Mathematical Models and Methods in Applied Sciences 等期刊发表10余篇论文,以及一篇Springer专著即将出版。

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