报告题目：A second order accurate, decoupled numerical scheme for magnetohydrodynamic equations

报 告 人：王成教授（美国麻省大学达特茅斯分校）

报告时间：2021年11月18日(周四) 10:00-12:00

Zoom网址：https://umassd.zoom.us/j/6339263022

密码：123456

报告摘要：A temporally second-order accurate, fully discrete finite element method is proposed and analyzed for the magnetohydrodynamic (MHD) equations. A modified Crank-Nicolson method is used to discretize the model and appropriate semi-implicit treatments are applied to the fluid convection term and two coupling terms. These semi-implicit approximations result in a linear system with variable coefficients for which the unique solvability can be proved theoretically. In addition, a decoupling projection method of the Van Kan type is used in the Stokes solver, which computes the intermediate velocity field based on the gradient of the pressure from the previous time level, and enforces the incompressibility constraint via the Helmholtz decomposition of the intermediate velocity field. The energy stability ofthe scheme is theoretically proved, in which the decoupled Stokes solver needs to be analyzed in details. Optimal-order convergence is proved for the proposed decoupled projection finite element scheme. Numerical examples are provided to illustrate the theoretical results.

报告人简介：王成，1993年毕业于中国科技大学获数学学士学位，2000年在美国坦普尔大学获得博士学位,。2000-2003年在美国印尼安纳大学做博士后，2003-2008年在美国田纳西大学任助理教授，2008-2012年在美国麻省大学达特茅斯分校任助理教授，2012年晋升为副教授，2019年晋升为教授。主要研究领域是应用数学，包括数值分析、偏微分方程、流体力学、计算电磁学等。在Journal of Computational Physics，SIAM Journal on Numerical Analysis，IMA Journal of Numerical Analysis等期刊上发表论文五十多篇。