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"九章讲坛"第143讲 — 邹青松 教授

日期:2019-07-24点击数:

应数学与统计学院伍渝江教授和宋伦继副教授的邀请,中山大学邹青松教授将于2019年7月28日访问数学与统计学院,期间将举办学术报告。

题   目:A Linear Finite Element Method for a Second Order Elliptic Equation in Non-Divergence Form with Cordès Coefficients

地   点:齐云楼911报告厅.

时   间:7月28日 上午10:30开始.

Abstract: In this talk, we present a $C^0$ linear finite element method for second order elliptic equations in non-divergence form. The proposed method is based on a symmetric weak formulation derived from a least- squares functional. Instead of applying $H^2$ or mixed elements, some popular post-processing gradient recovery operators are employed to approximate the discrete Hessian matrix of finite element functions. Due to the low degrees of freedom of linear element, the implementation of the proposed scheme is easy and straightforward. The rotation of the recovery gradient has been added as a penalty term to ensure the stability of the new numerical scheme. Optimal error estimate is shown in a discrete $H^2$ semi-norm. Furthermore, the proposed numerical method has been applied to the fully nonlinear Monge-Amp\`{e}re equation. Numerical experiments of problems with non-smooth and discontinuous coefficients over convex and non-convex domains have been presented to confirm the theoretical findings and robustness of the numerical approach. The numerical results indicate that our error estimates in standard $L^2$ norm and $H^1$ semi-norm are optimal, and the recovered numerical gradient converges to the exact one with a superconvergent order.


邹青松教授介绍

邹青松,中山大学数据科学与计算机教授, 广东省计算数学学会副理事长,期刊 Int. J.Numer. Anal. & Mod.编委,洪堡学者。长期从事偏微分方程前沿数值方法领域的研究工作,特别是有限体积法领域的工作,在SIAM J. Numer. Anal.,Math. Comp,Numer. Math. J. Sci Comp.等杂志上共发表论文近50篇。

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甘肃省高校应用数学与复杂系统省级重点实验室

数学与统计学院

萃英学院

2019年7月24日