题目：Optimal $L^2$ error estimates of unconditionally stable FE schemes for the Cahn-Hilliard-Navier-Stokes system.

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 super convergence 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.

报告人：王冀鲁 哈尔滨工业大学（深圳）

报告时间：2024年5月30日 下午 2:30-4:00

报告地点：腾讯会议：738-658-104 点击链接入会，或添加至会议列表：https://meeting.tencent.com/dm/T51GHNaYEMel

个人简介：王冀鲁，哈尔滨工业大学（深圳）教授，博导，曾入选国家级青年人才计划。2015 年在香港城市大学获博士学位，2016-2018年在佛罗里达州立大学从事博士后研究工作，2018-2019 年在密西西比州立大学担任访问助理教授。曾在北京计算科学研究中心任特聘研究员，她的研究课题主要集中在偏微分方程数值解，具体包括关于浅水波方程、多孔介质中不可压混溶驱动模型、薛定谔方程以及分数阶方程有限元方法的误差估计，研究成果发表在 《Numer. Math》、《SIAM J. Numer. Anal.》、《Math. Comput.》、《J. Comput. Phys.》、《SIAM J. Control Optim.》等计算数学权威期刊，目前分别主持和参与国家自然科学基金面上项目和重点项目。