主持人：郑海标 副教授
报告时间：2020年8月12日16:00- 17:00
报告平台：腾讯会议 房间号：610 134 519

报告人介绍：
　　陈洁副教授，博士生导师，南京大学 学士、硕士，南洋理工大学 博士；2011-2012年香港科技大学 博士后，2012-2013年沙特国王大学 博士后；2013年起在西安交通大学数学与统计学院工作，2019年进入西交利物浦大学工作。研究方向包括有限元方法，计算流体力学，油藏模拟。在Mathematics of Computation, Journal of computational physics, International Journal for Numerical Methods in Engineering等国际权威期刊上发表论文二十余篇。 2019年，第8届华人数学家大会45分钟邀请报告。

报告内容摘要：
A frame work of the mixed generalized multiscale finite element method (GMsFEM)for solving Darcy’s law in heterogeneous media is studied in this talk. Our approach approximates pressure in multiscale function space that is between fine-grid space and coarse-grid space and solves velocity directly in the fine-grid space. To construct multiscale basis functions for each coarse-grid element, three types of snapshot space are raised. The first one is taken as the fine-grid space for pressure and the other two cases need to solve a local problem on each coarse-grid element. We describe a spectral decomposition in the snapshot space motivated by the analysis to further reduce the dimension of the space that is used to approximate the pressure. Since the velocity is directly solved in the fine-grid space, in the linear system for the mixed finite elements, the velocity matrix can be approximated by a diagonal matrix without losing any accuracy. Thus it can be inverted easily. This reduces computational cost greatly and makes our scheme simple and easy for application. Moreover, the proposed method preserves the local mass conservation property that is important for subsurface problems. Numerical examples are presented to illustrate the good properties of the proposed approach. If offline spaces are appropriately selected, one can achieve good accuracy with only a few basis functions per coarse element according to the numerical results.