报告题目：A Low Order Divergence-free H(div)-conforming Finite Element Method for Stokes Flows

主 讲 人：芮洪兴

单 位：山东大学

时 间：12月9日16:00

腾 讯 ID：532935906

摘 要：

In this paper, we propose a P1⊕RT0 - P0 discretization of the Stokes equations on general simplicial meshes in two/three dimension, which yields an exactly divergence-free and pressure independent velocity approximation with optimal order. Our method has the following features. Firstly, the global number of the degrees of freedom of our method is the same as the low order Bernardi and Raugel (B-R) finite element method (Bernardi and Raugel, 1985), while the number of the non-zero entries of the former is about half of the latter in the velocity-velocity region of the coefficient matrix. Secondly, our method can be easily transformed into a pressure-robust and stabilized P1-P0 discretization for the Stokes problem via the static condensation of the RT0 component, which has a much smaller number of global degrees of freedom. Numerical experiments illustrating the robustness of our method are also provided.

简 介：

芮洪兴，教授，博士生导师。主要研究偏微分方程数值解法、科学与工程计算、油水资源数值方法及应用等。在计算数学三大顶级期刊Numer Math、SIAM J Numer Anal、Math Comp，流体力学顶级期刊J Fluid Mech等发表多篇高水平论文。承担国家自然科学基金重点项目、面上项目、中石化石油勘探院开发研究院外协国家重大科技专项课题等10余项。曾获教育部自然科学奖一等奖、山东省自然科学奖二等奖（首位）等。现任中国计算物理常务理事、山东省数学会计算数学专委会主任，曾任中国工业与应用数学学会常务理事、中国计算数学学会常务理事等。