A 3D Conforming-Nonconforming Mixed Finite Element for Solving Symmetric Stress Stokes Equations

Abstract

We propose a 3D conforming-nonconforming mixed finite element for solving symmetric stress Stokes equations. The low-order conforming finite elements are not inf-sup stable. The low-order nonconforming finite elements do not satisfy the Korn inequality. The proposed finite element space consists of two conforming components and one nonconforming component. We prove that the discrete inf-sup condition is valid and the discrete Korn inequality holds uniformly in the mesh-size. Based on these results we give some numerical verification. In addition, this element is compared numerically with six other mixed finite elements.