报告题目：A virtual element method for linear elasticity

报告人：段火元

报告时间：2024年05月09日（周四）16:00开始

报告地点：腾讯会议（会议号：621876960）

报告摘要：The virtual elements are advantageous over the conventional finite elements of piecewise polynomials. The former does not need the shape function of the finite dimensional space and is easily adaptable to arbitrarily-shaped polygonal or polyhedral elements and to interfacial boundaries of the underlying interfacial problems. A new virtual element is proposed for numerically solving the linear elasticity problem. In the method, we adopt the virtual elements constructed from the Poisson equation, together with some intrinsic stabilizations from the virtual element method of the Poisson equation of Dirichlet boundary condition. The method is new. We prove the stability and obtain the error estimates. The stability and error estimates are uniform in the Lame coefficient. As a result, the method is uniformly convergent. Moreover, the error estimates are optimal. Numerical results are provided.

报告人简介：段火元，武汉大学教授，博士生导师。曾经在新加坡国立大学2003年-2008年、2009年，在英国邓迪大学2008-2009 担任研究员。2009年-2013年南开大学数学科学学院教授，博士生导师。主要研究领域：偏微分方程数值解、科学计算。已发表论著六十多篇，一些论文发表在计算数学领域知名学术期刊SIAM Journal on Numerical Analysis, Mathematics of Computation, Numerische Mathematik, SIAM Journal on Scientific Computing, Journal of Computational Physics, IMA Journal of Numerical Analysis等。