讲座主题：Analysis of two-grid methods for miscible displacement problem by mixed finite element methods

专家姓名：陈艳萍

工作单位：华南师范大学

讲座时间：2017年6月26日9:00

讲座地点：数学院大会议室

主办单位：bob体育在线app数学与信息科学学院

内容摘要：

The miscible displacement of one incompressible fluid by another in a porous medium is governed by a system of two equations. One is elliptic form equation for the pressure and the other is parabolic form equation for the concentration of one of the fluids. Since only the velocity and not the pressure appears explicitly in the concentration equation, we use a mixed finite element method for the approximation of the pressure equation. In order to find a stable finite element discretization method method, we use different discretization method for the concentration equation, such as finite element method with characteristic; mixed finite element method with characteristic; expanded mixed finite element method with characteristic etc. To linearize the discretized equations, we use one (two) Newton iterations on the fine grid in our methods. Firstly, we solve an original non-linear coupling problem. Then, solve a linear system on the fine grid and while in second method we make a correction on the coarse grid between one (two) Newton iterations on the fine grid. We obtain the error estimates of two-grid method, it is shown that coarse space can be extremely coarse and we achieve asymptotically optimal approximation. Finally, numerical experiment indicates that two-grid algorithm is very effective.

主讲人介绍：

陈艳萍，华南师范大学二级教授、中国工业与应用数学学会油水资源数值方法专业委员会副主任。广东省计算数学学会副理事长。2008 年被聘为广东省高等学校珠江学者特聘教授，2005 年享受国务院颁发的政府特殊津贴，2012 年获广东省科学技术二等奖、 2011 年获湖南省自然科学一等奖、2008 年获教育部自然科学一等奖、2004 年获湖南省科学技术进步二等奖。入选爱思唯尔 2014年、2015年和 2016年中国高被引学者榜单。连续主持 6 项国家自然科学基金面上项目和 1 项国家自然科学基金重大研究计划“高性能科学计算的基础算法与可计算建模”培育项目。