报告时间：2023/6/20 16:00—17:00

报告地址：格物楼数学研究中心528报告厅

报告题目：Recovery based finite element methods for nondivergence form PDEs

报告摘要：In this talk, we will consider the numerical approximation of the non-divergence form PDEs with Cordes coefficients. In that case, the well posedness of the model problems can be viewed as the well posedness of a variational problems on H_0^1 \cap H^2. We construct a new recovery operator to overcome the difficulty that the vanishment of the piecewise second derivative of the linear finite element function. We will introduce some properties of this new recovery operator, especially the consistency of the finite element function that is hard to derive for the classical gradient recovery operators. Finally we use the new gradient recovery operator to construct linear finite element methods for the model problems and get the Cea's type error estimation of the numerical schemes.

报告人简介：郭海龙，2007年和2010年分别本科和硕士毕业于湖南师范大学、北京大学, 2015年博士毕业于美国韦恩州立大学，于2015年到2018年在美国加州大学圣塔芭芭拉分校任访问助理教授，2018年加入澳大利亚墨尔本大学，先后历任讲师和副教授。主要研究兴趣包括有限元超收敛后处理、界面问题的数值方法、机器学习算法等，在Comput. Methods Appl. Mech. Engrg., J. Comput. Phys., Math. Models Methods Appl. Sci., Math. Comp., Numer. Math., SIAM J. Numer. Anal., SIAM J. Sci. Comput. 等主流期刊发表论文20多篇。