T-coercivity for solving Stokes problem with nonconforming finite elements

TL;DR

This paper analyzes the stability of nonconforming finite element discretizations for the Stokes problem using T-coercivity, providing explicit stability constants and demonstrating the significance of divergence-free velocity reconstruction through numerical results.

Contribution

It introduces a T-coercivity framework for analyzing nonconforming finite element methods for the Stokes problem, including explicit stability constants.

Findings

Explicit stability constants for the discretization are derived.

Numerical results highlight the importance of divergence-free velocity reconstruction.

The T-coercivity approach enhances understanding of stability in nonconforming methods.

Abstract

We propose to analyse the discretization of the Stokes problem with nonconforming finite elements in light of the T-coercivity (cf. [1] for Helmholtz-like problems, see [2], [3] and [4] for the neutron diffusion equation). We propose explicit expressions of the stability constants. Finally, we give numerical results illustrating the importance of using divergence-free velocity reconstruction.