東大数値解析セミナー (UTNAS) 第147回

東京大学大学院数理科学研究科と情報理工学系研究科では,本年度も数値解析セミナーを定期的(月に1,2回程度)に開催致します.
多くの皆様のご参加をお待ち申し上げます.

講演者
Bernardo Cockburn (University of Minnesota, Distinguished McKnight University Professor)

題目
The transformation of stabilizations into spaces for Galerkin methods for PDEs

概要
We describe a novel technique which allows us to transform the terms which render Galerkin methods stable into spaces (JJIAM, 2023). We begin by applying this technique to show that the Continuous and Discontinuous Galerkin (DG) methods for ODEs produce the very same approximation of the time derivative, and use this to obtain superconvergence points of the DG method. We then apply this technique to mixed methods for second-order elliptic equations to show that they can always be recast as hybridizable DG  (HDG) methods. We then show that this recating makes the implementation from 10% to 20% better for polynomial degrees ranging from 1 to 20.We end by sketching or ongoing and future work.