Abstract: Numerical solutions of partial differential equations whose coefficients are discontinuous along some interface with complex geometry are challenging in practical applications. In this talk we first develop an adaptive high-order unfitted finite element method based on an hp-reliable and efficient residual type a posteriori error estimate on Cartisian K-meshes for elliptic interface problems. The crucial ingredient is a novel hp-domain inverse estimates which allow us to prove the stability of the finite element method under practical interface resolving mesh conditions and prove the lower bound of the a posteriori error estimate. The proposed high-order unfitted finite element method is then extended to three dimensional time-harmonic electromagnetic interface problems. This talk is based on joint works with Ke Li and Xueshuang Xiang.

报告人简介：陈志明，中国科学院数学与系统科学研究院研究员。主要从事数值分析和科学计算的研究。2001年获冯康科学计算奖，2009年获国家自然科学二等奖，2015年获中国数学会陈省身数学奖。2006年在国际数学家大会上做邀请报告。2017年当选中国科学院院士。