Hongxing Rui, Professor, School of Mathematics, Shandong University

Wei Gong, Associate Professor

A divergence-free H(div)-conforming finite element method for Stokes flows

9:00-10:00 November 3(Thursday), Tencent Meeting ID: 365-261-634

In this talk, we will propose in detail a divergence free discretization method for the Stokes equations based on P1⊕RT0 - P0 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: The global number of the degrees of freedom is the same as the low order Bernardi-Raugel element, 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, the 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 and a posterior error estimate are obtained. Applications to solve the Stokes optimal control problem and the interface problems, and the idea for constructing high order divergence-free element   are briefly introduced. Numerical experiments illustrate the robustness and accuracy of our method.