A new family of stable mixed finite elements for the 3D Stokes equations

A new family of stable mixed finite elements for the 3D Stokes equations

A natural mixed-element approach for the Stokes equations in the velocity-pressure formulation would approximate the velocity by continuous piecewise-polynomials and would approximate the pressure by discontinuous piecewise-polynomials of one degree lower. However, many such elements are unstable in 2D and 3D. This paper is devoted to proving that the mixed finite elements of this Pk-Pk−1 type ...

Stable finite elements for the Navier-Stokes equations

A New Family of Mixed Finite Elements for Elasticity

In this thesis, we introduce a new finite element method to discretize the equations of elasticity. It is analyzed thoroughly both in the infinite-dimensional and in the discrete setting, where finite element schemes of arbitrary order are presented. As the main result of this work, we prove that the new method is locking-free with respect to volume and shear locking, i.e that it is applicable ...

A Stable Finite Element for the Stokes Equations

We present in this paper a new velocity-pressure finite element for the computation of Stokes flow. We discretize the velocity field with continuous piecewise linear functions enriched by bubble functions, and the pressure by piecewise linear functions. We show that this element satisfies the usual inf-sup condition and converges with first order for both velocities and pressure. Finally we rel...

Stabilization of Low-order Mixed Finite Elements for the Stokes Equations

We present a new family of stabilized methods for the Stokes problem. The focus of the paper is on the lowest order velocity-pressure pairs. While not LBB compliant, their simplicity and attractive computational properties make these pairs a popular choice in engineering practice. Our stabilization approach is motivated by terms that characterize the LBB “deficiency” of the unstable spaces. The...