講座主題：Analysis of two-grid methods for miscible displacement problem by mixed finite element methods
專(zhuān)家姓名：陳艷萍
工作單位：華南師范大學(xué)
講座時(shí)間：2017年6月26日9:00
講座地點(diǎn)：數(shù)學(xué)院大會(huì)議室
主辦單位：煙臺(tái)大學(xué)數(shù)學(xué)與信息科學(xué)學(xué)院
內(nèi)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(xué)二級(jí)教授、中國(guó)工業(yè)與應(yīng)用數(shù)學(xué)學(xué)會(huì)油水資源數(shù)值方法專(zhuān)業(yè)委員會(huì)副主任。廣東省計(jì)算數(shù)學(xué)學(xué)會(huì)副理事長(zhǎng)。2008 年被聘為廣東省高等學(xué)校珠江學(xué)者特聘教授，2005 年享受?chē)?guó)務(wù)院頒發(fā)的政府特殊津貼，2012 年獲廣東省科學(xué)技術(shù)二等獎(jiǎng)、 2011 年獲湖南省自然科學(xué)一等獎(jiǎng)、2008 年獲教育部自然科學(xué)一等獎(jiǎng)、2004 年獲湖南省科學(xué)技術(shù)進(jìn)步二等獎(jiǎng)。入選愛(ài)思唯爾 2014年、2015年和 2016年中國(guó)高被引學(xué)者榜單。連續(xù)主持 6 項(xiàng)國(guó)家自然科學(xué)基金面上項(xiàng)目和 1 項(xiàng)國(guó)家自然科學(xué)基金重大研究計(jì)劃“高性能科學(xué)計(jì)算的基礎(chǔ)算法與可計(jì)算建模”培育項(xiàng)目。
