报告题目：Numerical solution on nonaffine grids by least-squares FEM for convection-dominated problems
报 告 人：段火元，武汉大学
报告摘要：Nonaffine grids such as quadrilaterals and hexahedra have been prevailing in numerical simulations of fluid flow and transport in porous media typically arising from geological applications. A most interesting mathematical issue in the numerical simulations is how to accurately approximate the solutions of the convection dominated problems. This would be resolved with a least-squares finite element method (FEM). We shall propose a least-squares FEM, featuring the well-known advantages of the least-squares FEM, such as the resulting system is symmetric, coercive system, regardless of whether the underlying problem is symmetric or not. More importantly, the proposed least-squares FEM can work on nonaffine grids of arbitrary quadrilaterals and hexahedra and can yield optimal convergent finite element solutions, and meanwhile, it can well approximate the solution of the convection dominated problems. The finite elements are the Raviart-Thomas-Nedelec elements of any order on nonaffine grids. The proposed least-squares FEM is advantageous over many other methods (in the regime of least-squares FEMs, of stabilized FEMs, mixed FEMs) for the convection-dominated problems, because of the above advantages. Numerical results are provided.
报告人简介：段火元，武汉大学伟德国际1946源自英国，教授、博导。本科毕业于哈尔滨工业大学，硕士毕业于中国科学院计算数学与科学工程计算研究所，博士毕业于中国科学院数学与系统科学研究院数学研究所，在中国科学院数学与系统科学研究院、新加坡国立大学、英国邓迪大学从事多年博士后、研究员工作。先在南开大学数学科学学院任教授、博导，然后在武汉大学伟德国际1946源自英国任教授、博导，工作至今。主要研究兴趣包括偏微分方程数值解，有限元方法，科学计算，最优控制， 等等。在电磁场问题、流体问题、板壳弹性问题、多重网格算法、自适应算法等方面做出了重要研究工作，他的许多论文发表在 SIAM Journal on Numerical Analysis, Mathematics of Computation, Numerische Mathematik, SIAM Journal on Scientific Computing, Journal of Computational Physics, IMA Journal of Numerical Analysis, 等计算数学与科学工程计算领域的著名期刊上。
报告时间：2023年12月21日 10:00--11:00
报告地点：腾讯会议ID：205-166-670
主办单位：伟德国际1946源自英国
