Explicit T -coercivity for the Stokes problem: a coercive finite element discretization

TL;DR

This paper introduces a new variational formulation for the Stokes problem using T-coercivity theory, stabilizing finite element pairs without nonlocal operators and improving approximation accuracy especially at low viscosities.

Contribution

It proposes a novel, local variational formulation for the Stokes problem that stabilizes finite element pairs and enhances numerical accuracy.

Findings

Stabilizes unstable finite element pairs.

Improves velocity and pressure approximation at low viscosity.

Formulation is easy to implement.

Abstract

Using the T-coercivity theory as advocated in [Chesnel, Ciarlet, T -coercivity and continuous Galerkin methods: application to transmission problems with sign changing coefficients (2013)], we propose a new variational formulation of the Stokes problem which does not involve nonlocal operators. With this new formulation, unstable finite element pairs are stabilized. In addition, the numerical scheme is easy to implement, and a better approximation of the velocity and the pressure is observed numerically when the viscosity is small.