报告题目： Locking-free finite element approximation to three-dimensional quasi-static electroporoelasticity equations
报 告 人：Cao Yanzhao 教授 奥本大学
讲授时间：2025年6月8日，14:00--15:00
授课地点：数学楼3楼研讨室6
校内联系人：邹永魁 zouyk@jlu.edu.cn
Abstract：The electroporoelasticity model, which comprises of Maxwell's equations with Biot's equations, plays a critical role in many fields such as oil-gas exploration, water conservancy exploration, earthquake early warning and some other areas in geophysics, etc. Sometimes, numerical approximation may exhibit Poisson locking when the Lam\'{e} constant becomes large and meanwhile the divergence of exact solution is small. In this work, we establish the well-posedness and propose a locking-free finite element approximation to three-dimensional quasi-static electroporoelasticity equations. We apply N\'{e}d\'{e}lec elements, nonconforming Crouzeix-Raviart elements and Lagrange elements together with backward Euler method to construct a fully discretized scheme, and then we derive uniform error estimates along with first-order convergence with respect to the Lam\'{e} constant. We prove that our numerical method inherits an asymptotic behavior from the original equations that the divergence of the approximate displacement tends to zero as the Lam\'{e} constant goes to infinity, ensuring the locking-free property of the algorithm. Numerical experiments are presented to validate our theoretical findings.
报告人简介：曹延昭教授，1983年毕业于吉林大学数学系，1996年获弗吉尼亚理工学院数学博士学位，现任美国奥本大学数学与统计学系 Don Logan endowed chair professor.应用与工业数学学会（SIAM）美国东南地区分会主席。主要从事偏微分方程和积分方程数值解法、随机偏微分方程数值解、非线性滤波、不确定性量化等领域的研究，部分研究成果发表在《SIAM J. Numer. Anal.》、《Numer. Math.》、《Math. Comp.》、《IMA J. Numer. Anal.》等计算数学顶级期刊上。
