报告题目：Polygonal staggered DG method for flows in porous media
报告人：Eun-Jae Park 韩国延世大学
时间：2024年 08月29日（星期四）2:30-3:15
地点: 正新楼209
校内联系人：王瑞姝 wangrs_math@jlu.edu.cn
报告摘要：In this talk, we first present the staggered discontinuous Galerkin method on general meshes for the Poisson equation. Then, we present a staggered DG method for a five-field formulation of the Biot system of poroelasticity on general polygonal meshes. Elasticity is equipped with stress-displacement-rotation formulation with weak stress symmetry for arbitrary polynomial orders, which extends the piecewise constant approximation developed in (L. Zhao and E.-J. Park, SIAM J. Sci. Comput. 42:A2158-A2181,2020). The proposed method is locking free and can handle highly distorted grids possibly including hanging nodes, which is desirable for practical applications. We prove the convergence estimates for the semi-discrete scheme and fully discrete scheme for all the variables in their natural norms. In particular, the stability and convergence analysis do not need a uniformly positive storativity coefficient. Moreover, to reduce the size of the global system, we propose a five-field formulation based fixed stress splitting scheme, where the linear convergence of the scheme is proved. Several numerical experiments are carried out to confirm the optimal convergence rates and the locking-free property of the proposed method.
报告人简介：Eun-Jae Park 是韩国延世大学教授。主要的研究方向有数值分析、科学计算、区域分解方法、偏微分方程数值方法、并行计算、多尺度计算等。在 Math. Comp., Numer. Math., J. Comput. Phys.等期刊发表论文90余篇。
