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Convergence analysis of a fully discrete scheme for incompressible vector potential MHD systems

讲座摘要

We investigate a fully discrete finite element scheme for the three dimensional incompressible magnetohydrodynamic problem based on magnetic vector potential formulation. The formulation enjoys the novel feature that it can always produce an exactly divergence-free magnetic induction discretized solution. Using a mixed finite element approach, we discretize the model by the fully discrete semi-implicit Euler scheme with the velocity and the pressure approximated by stable MINI finite elements and the magnetic vector potential by Nedelec edge elements.  Convergence analysis and error estimates for the velocity and the magnetic vector potential are rigorously established. Finally, several numerical experiments are presented to illustrate the convergence properties of the numerical scheme.


个人简介
毛士鹏,中国科学院数学与系统科学研究院研究员、博士生导师。中国科学院大学岗位教授。2008 年博士毕业于中国科学院数学与系统科学研究院, 2008-2012 先后在在法国国家信息自动化研究院(INRIA)以及在瑞士苏黎世高工(ETH Zurich)做博士后。主要研究兴趣为有限元方法及其应用,自适应算法, 计算流体力学和磁流体力学等。在 Math. Comp., Numer. Math.、SIAM. J. Numer. Math., SIAM J.Sci.Comput., Math. Model Meth. Appl. Sci. (M3AS)等 SCI 杂志上发表论文70 余篇.