报告题目：An Over-Penalized and Stabilized Weak Galerkin Method for Parabolic Interface Problems with Time -dependent Coefficients

报 告 人：宋伦继教授（兰州大学）

报告时间：2022年11月24日  14:30

报告地点：腾讯会议（120441815）

报告摘要：

Based on the idea of classical discontinuous Galerkin and weak Galerkin finite element methods, we introduce an over-penalized term in the new scheme as a part of stabilization for solving parabolic interface problems. From the double-valued functions defined on interior edges of elements, it is natural to generate jumps of the over-penalized term. An over-penalized and stabilized weak Galerkin (OPSWG) finite element method can be applied very well to interface problems with general imperfect interface. Importantly, the diffusion coefficients of the interface problems depend on both temporal and spacial variables, not only limited in space as usual. With the use of $(P_ k(K),P_ {k-1}(e), [P_ {k-1}(K)]^d)$ elements, semi-discrete and fully discrete schemes with backward Euler approximation in time are presented, and then the semi-discrete one is analyzed to be unconditionally stable. To analyze error estimates of semi-discrete and fully discrete schemes directly by error equation, we can just have optimal convergence order in energy norm. By virtue of the introduction of an elliptic projection operator, optimal error estimates of those schemes in $L^2$ norm can be proved. Numerical examples are given to validate the efficiency and optimal convergence orders of the new schemes.

报告人简介：

宋伦继，兰州大学数学与统计学院教授、应用数学博士、美国阿拉巴马大学博士后，首批国家一流本科课程负责人，2021获兰州大学隆基教育教学骨干奖。从事间断Galerkin方法及弱有限元方法的数值理论与计算、无界区域高频时谐波散射问题高精度算法研究、间断类型有限元解的PPR梯度重构方法等研究。在J. Comput. Phys., J. Sei. Comput, Appl. Numer. Math.等国内外学术期刊发表学术论文30余篇，主持国家自然科学基金面上项目，结题国家自然科学基金、省级项目、中央高校基本科研项目等7项。