报告题目：A new two-level defect-correction method for the steady Navier–Stokes equations
报告人： 尚月强
工作单位：西南大学数学与统计学院
报告时间：2021-11-14 8:30-10:30
腾讯会议ID：870 866 180
报告摘要：In this talk, I will present a new defect-correction method based on subgrid stabilization for the simulation of steady incompressible Navier–Stokes equations with high Reynolds numbers. The method uses a two-grid finite element discretization strategy and consists of three steps: in the first step, a small nonlinear coarse mesh system is solved,and then, in the following two steps, two Newton-linearized fine mesh problems which have the same stiffness matrices with only different right-hand sides are solved. The nonlinear coarse mesh system incorporates an artificial viscosity term into the Navier–Stokes system as a stabilizing factor, making the nonlinear system easier to resolve.While the linear fine mesh problems are stabilized by a subgrid model defined by an elliptic projection into lower-order finite element spaces for the velocity. Error bounds of the approximate solutions are estimated. Algorithmic parameter scalings are derived from the analysis. Effectiveness of the proposed method is also illustrated by some numerical results.
报告人简介：尚月强，男，西南大学数学与统计学院教授、博士生导师。2006年7月毕业于贵州师范大学计算数学专业，获理学硕士学位；2009年12月毕业于西安交通大学计算数学专业，获理学博士学位；2010年10月年至2011年10月在韩国仁荷大学做博士后研究，先后受邀到瑞典于默奥大学、林奈大学、瑞典国家高性能计算中心访学。主要从事偏微分方程数值解、计算流体力学和并行计算方面的研究，研究兴趣包括流体力学中的高效（并行）数值方法，并行数值代数，有限元方法，两重网格方法，区域分解算法等。主持完成了国家自然科学基金、教育部留学回国人员基金、省级科研基金项目共10余项， 在《J. Comput. Phys.》《Comput. Methods Appl. Mech. Engrg.》《J. Sci. Comput.》《中国科学：数学》等国内外知名期刊发表学术论文80余篇，其中SCI收录50余篇。
