A conservative stable finite element method for Stokes flow and nearly incompressible linear elasticity on rectangular grid

In this paper, we discuss finite element methods for the incompressible Stokes problem and the nearly incompressible linear elasticity problem. Specifically, we present a finite element pair for the incompressible Stokes problem, which satisfies the discrete inf-sup condition and the discrete Korn's inequality, and moreover, which is element-wise conservative. The pair provides a locking-free method for the nearly incompressible linear elasticity problem without reduced integration.