講座主題：Analysis of two-grid methods for miscible displacement problem by mixed finite element methods
專家姓名：陳艷萍
工作單位：華南師范大學
講座時間：2017年6月26日9:00
講座地點：數學院大會議室
主辦單位：煙臺大學數學與信息科學學院
內容摘要：
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.
主講人介紹：
陳艷萍，華南師范大學二級教授、中國工業與應用數學學會油水資源數值方法專業委員會副主任。廣東省計算數學學會副理事長。2008 年被聘為廣東省高等學校珠江學者特聘教授，2005 年享受國務院頒發的政府特殊津貼，2012 年獲廣東省科學技術二等獎、 2011 年獲湖南省自然科學一等獎、2008 年獲教育部自然科學一等獎、2004 年獲湖南省科學技術進步二等獎。入選愛思唯爾 2014年、2015年和 2016年中國高被引學者榜單。連續主持 6 項國家自然科學基金面上項目和 1 項國家自然科學基金重大研究計劃“高性能科學計算的基礎算法與可計算建模”培育項目。
