報告題目：Polygonal staggered DG method for flows in porous media
報告人：Eun-Jae Park 韓國延世大學
時間：2024年 08月29日（星期四）2:30-3:15
地點: 正新樓209
校内聯系人：王瑞姝 wangrs_math@jlu.edu.cn
報告摘要：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.
報告人簡介：Eun-Jae Park 是韓國延世大學教授。主要的研究方向有數值分析、科學計算、區域分解方法、偏微分方程數值方法、并行計算、多尺度計算等。在 Math. Comp., Numer. Math., J. Comput. Phys.等期刊發表論文90餘篇。
