Dual-Mixed Finite Element Methods for the Navier-Stokes Equations

TL;DR

This paper introduces a mixed finite element method for the Navier-Stokes equations that treats stress as a primary variable, maintaining the equations' mathematical structure and developing suitable finite element spaces.

Contribution

It presents a novel mixed finite element formulation with stress as a primary variable, extending classical theory and satisfying inf-sup conditions.

Findings

Mathematically consistent variational formulation

Finite element spaces satisfying inf-sup conditions

Extension of classical theory to new formulation

Abstract

A mixed finite element method for the Navier-Stokes equations is introduced in which the stress is a primary variable. The variational formulation retains the mathematical structure of the Navier-Stokes equations and the classical theory extends naturally to this setting. Finite element spaces satisfying the associated inf-sup conditions are developed.