学术报告-陈黄鑫

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2021-12-16 08:42:00


学术报告


题      目:  Stabilized finite element methods for high order Laplace equation


报  告  人:陈黄鑫   教授  (邀请人:冷海涛 )

                                   厦门大学


时      间:2021-12-16  10:00-11:00


腾讯会议:678 167 386


报告人简介:

       陈黄鑫, 男,2011年从中国科学院数学与系统科学研究院获得博士学位,后进入厦门大学工作,现为厦门大学数学学院教授。研究兴趣集中在自适应有限元方法、多重网格方法、间断有限元方法和多孔介质流体输运等方面。在SIAM,Math. Comput., Numer. Math., ESAIM,CMAME,JCP, JSC.,IMA,Water Resour.Res.等计算数学一流期刊上发表论文三十余篇。主持国家自然科学基金面上、青年各一项。

摘      要:

      In this talk, we will introduce some new stabilized finite element methods for high order Laplace equation. Firstly, a new stabilized finite element scheme using element-wise stabilization will be introduced for the biharmonic equation on Lipschitz polyhedral domains. The proposed scheme doesn't involve any integration along mesh interfaces. This scheme can be easily implemented and produces positive definite linear system. Optimal convergences in both discrete $H^2$-norm and $L^2$-norm are derived. The scheme with its analysis will be further generalized to the von K\'arm\'an equation and the quad-curl problem. Moreover, we will also discuss a $C^0$ interior penalty method for the $m$th-Laplace equation.













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