1                                                                   

 New analysis and recovery technique of mixed FEMs for compressible miscible displacement in porous media

主讲人：孙伟伟

摘要：Numerical methods and analysis for compressible miscible flow in porous media have been investigated extensively in the last several decades. Amongst those methods, the lowest-order mixed method is the most popular one in practical applications. The method is based on the linear Lagrange approximation for the concentration and the lowest order (zero-order) Raviart–Thomas mixed approximation for the Darcy velocity/pressure. However, the existing error analysis only provides the first-order accuracy in L2-norm for all three physical components in spatial direction, which was proved under certain extra restrictions on both time step and spatial meshes. The analysis is not optimal for the concentration mainly due to the strong coupling of the system and the drawback of the traditional approach which leads to serious pollution to the numerical concentration in analysis. The main task of this paper is topresent a new analysis and establish the optimal error estimate of the commonly-used linearized lowest-order mixed FEM. In particular, the second-order accuracy for the concentration in spatial direction is proved unconditionally. Moreover, we propose a simple recovery technique to obtain a new numerical Darcy velocity/pressure of second-order accuracy by re-solving an elliptic pressure equation. Also we extend our analysis to a second-order time discrete scheme to obtain optimal error estimates in both spatial and temporal directions. Numerical results are provided to confirm our theoretical analysis and show the efficiency of the method.

主讲人简介：孙伟伟教授，珠江学者，于1991年在加拿大温莎大学取得博士学位，专业为应用数学。在加入北师港浸大之前，他在香港城市大学担任教授。孙伟伟教授的研究领域包括大规模科学与工程计算，尤其是非线性偏微分方程、数学建模和矩阵计算与应用。孙伟伟教授已发表SCI学术论文超过130篇，并在过去20年间得到了香港研究资助局(Hong Kong Research Grant Council)共18项作为项目负责人的科研经费支持。

邀请人：李东方

时间：2025年4月19日14：00—18：00

地点：逸夫科技楼南楼706