报告时间：2022年06月10日（星期五）14:00-15:00

报告地点：腾讯会议 276284200

报 告 人：宋伦继 副教授

工作单位：兰州大学

举办单位：数学与统计学院

报告简介：

Several new relaxed/over-penalized weak Galerkin (WG) methods have been proposed for second order elliptic, 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 $l\geq0$ 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 $\displaystyle\beta=1+\frac{4}{p}-p$ can be given in the energy norm. The stabilized WG method can be easily implemented without requiring any sufficiently large penalty factor.

报告人简介：

宋伦继，兰州大学数学与统计学院副教授、应用数学博士、美国阿拉巴马大学博士后，2020年首批国家一流本科课程负责人，2021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. Sci. Comput., Appl. Numer. Math.等国内外学术期刊发表学术论文30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。