报告题目：Hybrid high-order methods for the fourth-order problem

报告人：National Institute for Research in Digital Science and Technology (INRIA, France)，董兆楠 研究员

报告时间：2022年10月12日下午14:30-17:30

报告地点：腾讯会议(会议ID：365209742,会议密码：2022)

摘要：We start with a gentle introduction to the devising and analysis of hybrid high-order (HHO) methods for the biharmonic problem. In particular, we compare the proposed HHO methods to the literature, in particular to weak Galerkin methods. Then, we propose a hybrid high-order method (HHO) to approximate singularly perturbed fourth-order PDEs on domains with a possibly curved boundary. The two key ideas in devising the method are the use of a Nitsche-type boundary penalty technique to weakly enforce the boundary conditions and scaling of the weighting parameter in the stabilization operator that compares the singular perturbation parameter to the square of the local mesh size. With these ideas in hand, we derive stability and optimal error estimates over the whole range of values for the singular perturbation parameter, including the zero value for which a second-order elliptic problem is recovered. Numerical experiments illustrate the theoretical analysis.

报告人简介：Zhaonan (Peter) Dong is currently a permanent researcher (CRCN) at in the National Institute for Research in Digital Science and Technology (INRIA, France) since 10/2020. Before he moved to Paris, he used to be Lecturer at the Cardiff University (UK) from 01/2019 to 09/2020. he was a visiting researcher of the research group lead by Prof. Charalambos Makridakis at the IACM-FORTH (Greece). He was post-doc researcher at the University of Leicester (UK) from 10/2016 to 09/2018.  He obtained his PhD under the supervision of Prof. Emmanuil Georgoulis and Dr. Andrea Cangiani in 10/2016 at the University of Leicester.

His research interest is Numerical Methods for Partial Differential Equations. More specifically: continuous and discontinuous FEM, hp-version FEM, adaptive algorithms, multiscale methods, polygonal discretization methods, solver design. In the past several years, he has obtained one Springer Monograph and several papers accepted and published on leading journals: SIAM J. Numer. Anal.，SIAM J. Sci. Comput.， Math. Comp..