报告题目：Analysis of a class of globally divergence-free HDG methods for stationary Navier-Stokes equations

主讲人：谢小平

单位：四川大学

时间：12月7日10:00

腾讯会议：720-371-670

摘要：We analyze a class of globally divergence-free (and therefore pressure-robust) hybridizable discontinuous Galerkin (HDG) finite element methods for stationary Navier-Stokes equations. The methods use the Pk/Pk-1 (k\geq1) discontinuous finite element combination for the velocity and pressure approximations in the interior of elements, and piecewise Pk/Pk for the trace approximations of the velocity and pressure on the inter-element boundaries. We show that the uniqueness condition for the discrete solution is guaranteed by that for the continuous solution together with a sufficiently small mesh size. Based on the derived discrete HDG Sobolev embedding properties, we obtain optimal error estimates. Numerical experiments confirm the theoretical results.

简 介：谢小平，四川大学数学学院教授（博导），四川省学术和技术带头人，教育部新世纪优秀人才，德国洪堡学者。现兼任四川省普通本科高等学校数学类教学指导委员会秘书长,中国工业与应用数学学会油水资源数值方法专业委员会副主任委员，中国工业与应用数学学会高性能计算与数学软件专业委员会委员，中国仿真学会集成微系统建模与仿真专业委员会委员。主要从事偏微分方程数值解相关领域的研究工作。曾获教育部自然科学奖二等奖。