报告题目： Analysis of two-grid methods for miscible displacement problem by mixed finite element methods

报 告 人： 陈艳萍 教授

报告时间： 5月15（星期一）上午 10:00--11:00

报告地点： 上海师范大学（徐汇校区）10楼222室

简    介： 华南师范大学二级教授、博士生导师、广东省计算数学学会副理事长（2016-2020）、广东省计算科学重点实验室学术委员会委员。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，2004 年入选教育部首批新世纪优秀人才支持计划，2002 年评为教育部首批全国高等学校优秀骨干教师。2012 年获广东省科学技术二等奖（排第一）、2011 年获湖南省自然科学一等奖（排第三）、2008 年获教育部自然科学一等奖（排第三）、2004 年获湖南省科学技术进步二等奖（排第一）。

报告摘要： 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.

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