报告时间：2024年12月11日 10:00开始
报 告 人：郑海标（华东师范大学 副教授）
报告地点：9-218
报告题目：FEM-MsFEM for the Stokes-Darcy Model
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.
报告人简介：郑海标，华东师范大学副教授，博士生导师；西安交通大学 博士；美国匹兹堡大学联合培养博士研究生，英国剑桥大学访问学者；主要研究方向为多物理场耦合系统可计算建模及高性能算法；曾两次获陕西省科学技术奖二等奖（第二完成人）；主持国家自然科学基金三项；主持上海市应用培育项目一项；参与国家科技部重点研发专项一项。
