應(yīng)yl7703永利官網(wǎng)邀請(qǐng)，哈爾濱工業(yè)大學(xué)（深圳）王冀魯教授將于2024年8月16-19日訪問蘭州大學(xué)，期間舉辦專題學(xué)術(shù)報(bào)告，歡迎全校師生參加。

報(bào)告題目: Optimal L^2 error estimates of unconditionally stable FE schemes for the Cahn-Hilliard-Navier-Stokes system

報(bào)告摘要：The paper is concerned with the analysis of a popular convex-splitting finite element method for the Cahn-Hilliard-Navier-Stokes system, which has been widely used in practice. Since the method is based on a combined approximation to multiple variables involved in the system, the approximation to one of the variables may seriously affect the accuracy for others. Optimal-order error analysis for such combined approximations is challenging. The previous works failed to present optimal error analysis in $L^2$-norm due to the weakness of the traditional approach. Here we first present an optimal error estimate in $L^2$-norm for the convex-splitting FEMs. We also show that optimal error estimates in the traditional (interpolation) sense may not always hold for all components in the coupled system due to the nature of the pollution/influence from lower-order approximations. Our analysis is based on two newly introduced elliptic quasi-projections and the superconvergence of negative norm estimates for the corresponding projection errors. Numerical examples are also presented to illustrate our theoretical results. More important is that our approach can be extended to many other FEMs and other strongly coupled phase field models to obtain optimal error estimates.

時(shí) 間：2024年8月17日（星期六）11：30.

地 點(diǎn)：理工樓631

歡迎廣大師生光臨!

報(bào)告人簡(jiǎn)介

王冀魯，哈爾濱工業(yè)大學(xué)（深圳）教授，博導(dǎo)，曾入選國(guó)家級(jí)青年人才計(jì)劃，此前為北京計(jì)算科學(xué)研究中心特聘研究員。她的研究課題主要集中在偏微分方程數(shù)值解，具體包括關(guān)于淺水波方程、多孔介質(zhì)中不可壓混溶驅(qū)動(dòng)模型、薛定諤方程以及分?jǐn)?shù)階方程的數(shù)值方法，研究成果發(fā)表在 《Numer. Math》、《SIAM J. Numer. Anal.》、《Math. Comput.》、《SIAM J. Control Optim.》、《J. Comput. Phys.》等計(jì)算數(shù)學(xué)權(quán)威期刊，目前分別主持和參與國(guó)家自然科學(xué)基金面上項(xiàng)目和重點(diǎn)項(xiàng)目。

甘肅應(yīng)用數(shù)學(xué)中心

yl7703永利官網(wǎng)

萃英學(xué)院

2024年8月14日