报告人：郑海标副教授

报告题目：FEM-MsFEM for the Stokes-Darcy Model

主持人：杨畅

报告摘要：

This talk explores the application of the multiscale finite element method (MsFEM) to address steady-state and non-stationary Stokes-Darcy problems with BJS interface conditions in highly heterogeneous porous media. We assume the existence of multiscale features in the Darcy region and propose an algorithm for the multiscale Stokes-Darcy model. For the steady case, we employ MsFEM to construct permeability-dependent offline bases for efficient coarse-grid simulation in the offline phase, with this process conducted in parallel to enhance its efficiency. In the online phase, we use the Robin-Robin algorithm (FEM for Stokes, MsFEM for Darcy) to derive the model's solution. Subsequently, we conduct error analysis based on L2 and H1 norms, assuming certain periodic coefficients in the Darcy region. For the non-stationary case, we assume that permeability does not vary with time, making the method for generating basis functions similar to the steady-state case in offline phase and use partitioned time stepping algorithm for the non-stationary solution in online phase (FEM for Stokes, MsFEM for Darcy). Moreover, corresponding error analysis has also been proposed. To validate our approach, extensive numerical tests for both steady and non-stationary on highly heterogeneous media are presented, illustrating the results of the error analysis. 

报告时间：2024.08.03   8:00-12:00

报告地点：理学楼401室

报告人简介：郑海标，西安交通大学博士，华东师范大学副教授。主要从事不可压缩流动问题、多物理场耦合问题可计算建模及高性能算法研究，在SIAM系列、Comput. Meth. Appl. Mech. Eng.、J. Comput. Phy.等国际知名期刊发表高水平学术论文40余篇。曾两次获陕西省科学技术奖二等奖（第二完成人）奖励，在英国剑桥大学、美国匹兹堡大学、香港城市大学等多个大学交流访问。