报告题目：An efficient flux-variable approximation scheme for Darcy's flow
报 告 人：Young Ju Lee 教授
所在单位：Texas State University
报告时间：2023年12月06日 9:00-10:00
报告地点：腾讯会议：575-899-232
校内联系人：贾继伟 jiajiwei@jlu.edu.cn
报告摘要：We present an efficient numerical method to approximate the flux variable for the Darcy flow model. An important feature of our new method is that the approximate solution for the flux variable is obtained without approximating the pressure at all. To accomplish this, we introduce a user-defined parameter, which is typically chosen to be small so that it minimizes the negative effect resulting from the absence of the pressure, such as inaccuracy in both the flux approximation and the mass conservation. The resulting algebraic system is of significantly smaller degrees of freedom, compared to the one from the mixed finite element methods or least-squares methods. We also interpret the proposed method as a single step iterate of the augmented Lagrangian Uzawa applied to solve the mixed finite element in a special setting. Lastly, the pressure recovery from the flux variable is discussed and an optimal--order error estimate for the method is obtained. Number of examples are provided to verify the proposed theory and algorithm, some of which are from more realistic models such as SPE10.
报告人简介：Young Ju Lee is a Professor at Texas State University, Mathematics Department. He obtained his Ph.D degree at Penn State and had a prior faculty position at UCLA and Rutgers, The State University of New Jersey. His expertise is at the development of fast solver for partial differential equations. His current research focuses on development of structure preserving finite element discretization for PDE systems. His research has been funded by National Science Foundation and American Chemical Society. The current research is being funded by Korea Brain Pool program by National Research Foundation of Korea.
