讲座主题：Error estimates of EDG-HDG methods for the Stokes equations with Dirac measures

主讲人：冷海涛

工作单位：华南师范大学

活动时间：2021年4月22日 10：00-11:00

讲座地点：数学学院小会议室（303室）

主办单位：烟台大学数学与信息科学学院

内容摘要：

Abstract: 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

, and the pressure is discretized by polynomials of degree

. 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

-norm, and a posteriori error estimates for the velocity in in

-seminorm and the pressure in-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.

主讲人介绍：

冷海涛，博士毕业于华南师范大学，并于2018-2019年在香港中文大学做博士后，现为华南师范大学的副研究员。主要从事最优控制问题、对流扩散问题、分数阶等领域的快速算法研究。目前已在J. Sci. Comput., Appl. Math. Lett., Comput. Math. Appl等计算数学知名杂志发表论文十余篇。