报告题目：A relaxed weak Galerkin method for elliptic interface problems with low regularity

报告人：宋伦继 教授 兰州大学数学与统计学院

报告时间：2021年6月19日 10：30-11：30

报告地点：腾讯会议 会议 ID：877 874 999 会议密码：0619

校内联系人：柴世民 chaism@jlu.edu.cn

报告摘要：A new relaxed weak Galerkin (WG) method has been proposed for second order elliptic interface problems with low regularity solutions. We generalize the stabilizer from the weak Galerkin method based on a new relaxation index $\beta$, which can be tuned by the regularity of solution. The relaxed stabilization gives rise to considerable flexibility in treating weak continuity along interior element edges and interface edges. For solutions in Sobolev space $W^{l+1,p}$, with l≥0 and $p\in(1,2]$ rather than the usual case $p=2$, we derive convergence orders of the new WG method in the energy and $L^p$ norms under some regularity assumptions of the solution and an optimal selection of $\beta=1+\frac{4}{p}−p $ can be given in the energy norm. The stabilized WG method can be easily implemented without requiring any sufficiently large penalty factor. We will also introduce a new over-penalized weak Galerkin method and its applications.

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、美国阿拉巴马董事长物数学与高性能计算博士后，2020年首批国家一流本科课程负责人。从事非线性椭圆、抛物型偏微分方程的间断Galerkin方法数值理论和计算、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 梯度恢复技术等。在J. Comput. Phys., J. Sci. Comput., Appl. Numer. Math.等国内外学术期刊发表学术论文近30篇。主持国家自然科学青年基金、天元数学基金、省级项目、中央高校基本科研项目等6项。