Abstract

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. The 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, 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. A priori error estimates and a posterior error estimate are obtained. Numerical experiments illustrate the robustness and accuracy of our method. Numerical methods based one the same idea for the N-S equations are under consideration.

About the speaker

芮洪兴，山东大学数学学院教授、博士生导师、数学学院副院长。中国工业与应用数学学会常务理事兼油水资源数值方法专委会主任、中国计算物理学会常务理事，曾任中国计算数学学会常务理事。主要从事偏微分方程数值解法、科学与工程计算、渗流力学、油水资源数值模拟方法及应用软件开发等计算数学与应用数学研究。在有限元方法、混合元方法、有限体积元方法、特征线算法、区域分裂及并行算法、以及油水资源数值模拟方法研究方面发表论文150余篇，其中SCI收录100余篇。近年来芮洪兴教授承担、参与国家自然科学基金重大研究计划培育项目、面上项目、教育部博士点项目、科技部重大专项、中石化课题等20余项，先后获得山东省高校自然科学一等奖(2003) 、山东省科学技术奖自然科学二等奖(2015);并作为主要完成人获教育部自然科学一等奖 (2003)、水利部科技进步三等奖 (1998)、国家教委科技进步二等奖(1997)各一项。