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