报告人：冷海涛（华南师范大学）

时  间：5月11日下午02:30

地  点：厦大海韵园实验楼106报告厅

内容摘要:

In this talk, we present and analyze the hybridized, embedded-hybridized and embedded discontinuous Galerkin methods for the Stokes equations with Dirac measures. The velocity, the velocity traces and the pressure traces are approximated by polynomials of degree $k\geq 1$, and the pressure is discretized by polynomials of degree $k-1$. An attractive property, named divergence-free, is satisfied by these methods for the velocity field. Moreover, the velocity fields for hybridized and embedded-hybridized discontinuous Galerkin methods are $H$(div)-conforming, which means that a priori error estimates for the velocity do not depend on the pressure. Using duality argument and Oswald interpolation, a priori and a posteriori error estimates are obtained for the velocity in $L^2$-norm, and a posteriori error estimates for the velocity in $W^{1,q}$-seminorm and the pressure in $L^q$-norm are also derived. Finally, several numerical examples are provided to validate the theoretical analysis and show the performance of the obtained a posteriori error estimators.

个人简介：

冷海涛，华南师范大学青年英才（特聘副研究员）；2018年博士毕业于华南师范大学；2018-2019在香港科技大学做博士后。在杂交间断伽辽金方法、不可压流体、最优控制问题等领域发表文章十余篇。现正主持国家自然科学基金青年项目。

联系人：陈黄鑫