應(yīng)yl7703永利官網(wǎng)伍渝江教授和宋倫繼副教授的邀請(qǐng)，中山大學(xué)鄒青松教授將于2019年7月28日訪問yl7703永利官網(wǎng)，期間將舉辦學(xué)術(shù)報(bào)告。

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

地   點(diǎn)：齊云樓911報(bào)告廳.

時(shí)   間：7月28日 上午10:30開始.

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.

鄒青松教授介紹

鄒青松，中山大學(xué)數(shù)據(jù)科學(xué)與計(jì)算機(jī)教授， 廣東省計(jì)算數(shù)學(xué)學(xué)會(huì)副理事長(zhǎng)，期刊 Int. J.Numer. Anal. & Mod.編委，洪堡學(xué)者。長(zhǎng)期從事偏微分方程前沿?cái)?shù)值方法領(lǐng)域的研究工作，特別是有限體積法領(lǐng)域的工作，在SIAM J. Numer. Anal.，Math. Comp，Numer. Math. J. Sci Comp.等雜志上共發(fā)表論文近50篇。

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甘肅省高校應(yīng)用數(shù)學(xué)與復(fù)雜系統(tǒng)省級(jí)重點(diǎn)實(shí)驗(yàn)室

yl7703永利官網(wǎng)

萃英學(xué)院

2019年7月24日