报告题目：

A hypocoercivity-exploiting stabilised finite element method for Kolmogorov equation

报告人： 董兆楠研究员，法国国家信息与自动化研究所

报告时间：2025年4月23日上午9:30-11:30

报告地点：数学楼423会议室

报告摘要：

We propose a new stabilised finite element method for the classical Kolmogorov equation. The latter serves as a basic model problem for large classes of kinetic-type equations and, crucially, is characterised by degenerate diffusion. The stabilisation is constructed so that the resulting method admits a numerical hypocoercivity property analogous to the corresponding property of the PDE problem. More specifically, the stabilisation is constructed so that a spectral gap is possible in the resulting “stronger-than-energy” stabilisation norm, despite the degenerate nature of the diffusion in Kolmogorov thereby, the method has a provably robust behaviour as the “time” variable goes to infinity. We consider both a spatially discrete version of the stabilised finite element method and a fully discrete version, with the time discretisation realised by discontinuous Galerkin timestepping. Both stability and a priori error bounds are proven in all cases. Numerical experiments verify the theoretical findings.

报告人简介：

董兆楠，法国国家信息与自动化研究所（INRIA，Paris）研究员，主要研究方向包括continuous and discontinuous FEM、hp-version FEM、adaptive algorithms、multiscale methods、 polygonal discretization methods、hybrid high-order methods、solver design等。2016年10月在英国University of Leicester师从间断有限元方法专家Emmanuil Georgoulis教授和 Andrea Cangiani博士，获得应用数学博士，随后在英国University of Leicester从事博士后研究。 2019年在希腊国立数学研究院（IACM-FORTH）做访问学者，2019年11月至2020年9月在英国Cardiff University 数学系担任讲师。近年来在 SIAM Journal of Numerical Analysis、Mathematics of Computation、SIAM Journal on Scientific Computing等计算数学权威期刊上发表学术论文20余篇，并在Springer 出版社出版一部专著。

邀请人：晏文璟教授