计算与应用讨论班

报告题目：Sharp norm equivalence of mass lumping in Q_1 element in any high dimension

报  告  人：Dongwoo Sheen (Seoul National University & Xinjiang University)

时        间：2026年3月30日（星期一），下午16:00

地        点：海纳苑2幢206

摘     要：Mass lumping techniques have been widely used especially in time integration to obtain explicit methods. We establish the equivalence of the discrete ℓ^2-norm and the L^2-norm on the Q_1-finite element spaces (in any high dimension) is uniform in mesh size h, in both cases of uniform and nonuniform partitions. Several representation formulae for these norms are derived. Using these, accurate bounds between these two norms are obtained, which is our major contribution. Examples show that these bounds are sharp. As an important application, the equivalence is established between discrete h^1-norm and H^1 -norm. Numerical results will be presented. This is a joint work with Ma Peng (China U of  Petroleum-Beijing at Karamay), Yinnian He (Xi’an Jiaotong U), and Xinlong Feng (Xinjiang U).

报告人简介：Dongwoo Sheen received BA and MA at SNU in 1981 and 1983, and his PhD under the guidance of Prof. Jim Douglas, Jr. at Purdue University in 1991. Then he went to Pavia, Italy as a CNR postdoctoral fellow under Prof. Franco Brezzi’s guidance. He then went back to Purdue University as a post-doc. Since 1993, he worked for SNU until 2023. Currently he is a Professor Emeritus at SNU and a Distinguished Professor at Xinjiang University.

He held visiting professorship at the New South Wales University(1999), Purdue University(2006–2007), Texas A&M University(2013–2014), Kyoto University(2015), and the Ocean University of China (2023).

His research interests include Numerical Analysis and Scientific Computation in several application areas including fluid and solid mechanics, electrodynamics, math finance, and math biology. Specifically he has contributed in developing several fundamental Nonconforming Finite Element Methods and parallel algorithms based on Laplace Transform Methods.

He served as the President for several organization, including  Applied Math Forum, the East Asia Section of SIAM, the Korean Society for Math Biology, and the Korean Society of Computational Sciences.