报告题目： A posteriori error analysis for discontinuous Galerkin methods on polygonal and polyhedral meshes

摘要:  PDE models are often characterised by local features such as solution singularities/layers and domains with complicated boundaries and phase transitions. These special features make the design of accurate numerical solutions challenging or require a huge amount of computational resources. One way of achieving complexity reduction of the numerical solution for such PDE models is to design novel numerical methods which support general meshes consisting of polygonal/polyhedral elements, such that local features of the model can be resolved efficiently by adaptive choices of such general meshes. In this talk, we will present recent results on a new a posteriori error analysis for the dG method on general computational meshes consisting of polygonal/polyhedral (polytopic) elements with an arbitrary number of tiny faces. The new a posteriori error analysis first appeared in the literature and generalizes the known results for dG methods to admit an arbitrary number of irregular hanging nodes per element. Moreover, under certain practical mesh assumptions, the new error estimator of the dG method was proven to be available to incorporate essentially arbitrarily-shaped elements with an arbitrary number of faces or even curved faces. Finally, we will present the a posteriori error estimator of the space-time dG method for solving the Allen- Cahn problem and hp-DG for solving the biharmonic problems.

时间：2024年7月10日（星期三）上午10:00-11:30

地点：理学楼609报告厅

报告人简介：董兆楠，法国国家信息与自动化研究所（INRIA, France) 研究员。曾于2019年1月至2020年9月在卡迪夫大学（英国）担任讲师，于2016年10月至2018年9月在莱斯特大学（英国）担任博士后研究员。研究方向为偏微分方程的数值方法，具体包括：间断有限元方法、hp有限元法、自适应算法、多尺度方法，多边形离散化方法、求解器设计等。出版Springer专著一本，并在顶级期刊上发表了15篇论文包括 SIAM J. Numer. Anal., SIAM J. Sci. Comput., Math. Comp., IMA J. Numer. Anal.等。