Tianyuan Mathematical Center
in Southwest China

Introduction on conforming discontinuous Galerkin finite elements

报告题目:  Introduction on conforming discontinuous Galerkin finite elements

报告专家：张上游（美国特拉华大学）

报告时间：2023年3月9日上午10：00-11：00

报告地点：数学学院四楼409报告厅

摘要：

In all existing discontinuous Galerkin methods, the degree k polynomial solution converges at the optimal order only, i.e., order k plus 1 in L2 norm and order k in H1 norm. In the new conforming discontinuous Galerkin method, the numerical flux is no longer the average of two discontinuous functions on two sides of an edge or a triangle, but an average of four discontinuous functions nearby. With properly reconstructed trace and properly chosen spaces for the gradient and the Hessian, the CDG degree k polynomial solution converges at two-order and four-order above the optimal order for second order elliptic equations and fourth order elliptical equations, respectively,  i.e., order k plus 3 in L2 norm and order k plus 2 in H1 norm for second order elliptic equations, and order k plus 5 in L2 norm and order k plus 3 in H2 norm for fourth order elliptic equations. In other words, the CDG $C^{-1}$-$P_3$ solution is as good as the $C^1$-$P_7$ conforming finite solution in approximation.

报告人简介：

张上游获中国科技大学1977级数学学士和美国宾州州立大学1988年数学博士。之后在美国特拉华大学任教至今。张上游主要工作于计算数学的有限元方法构造和分析。在数学杂志上发表了160篇论文。其中一篇关于 Scott-Zhang插值（以其名字命名的算子在计算数学中广为引用） 的论文，在过去15年里几乎每年都列入《数学评论》的数学论文引用百强，在顶尖计算数学杂志《Math Comp》所有80年文章中总引用率排名第二。

邀请人：陈刚