In this talk, we present a robust discretization and solver developed for convection-dominated PDEs discretized on unstructured simplicial grids. The convection can be any one of the following operators: gradient, curl and divergence. The derivation of this schemes makes use of some intrinsic properties of differential forms and in particular some crucial identities from differential geometry. Both theoretical analysis and numerical experiments show that the new upwinding finite element schemes provide an accurate and robust discretization and a fast solver in many applications and in particular for simulation of magnetohydrodynamics systems when the magnetic Reynolds number Rm is large.

吴朔男，北京大学数学科学学院助理教授。分别于2009、2014年在北京大学获得学士学位和博士学位，2014至2018年在宾州州立大学从事博士后研究。研究方向:有限元方法和多重网格法的理论与应用，包括高阶椭圆型偏微分方程有限元方法、相场问题的建模和数值分析、磁流体中磁对流的稳定化方法、空间分数阶微分方程求解器