A multipoint vorticity mixed finite element method for incompressible Stokes flow

TL;DR

This paper introduces a novel mixed finite element method for incompressible Stokes flow that is efficient, divergence-free, and pressure robust, validated through theoretical analysis and numerical experiments.

Contribution

It presents a new finite element approach with one degree of freedom per element and facet, utilizing vorticity elimination for improved accuracy in Stokes flow simulations.

Findings

Discrete solution is pointwise divergence-free

Method is pressure robust

Convergence rates confirmed by numerical experiments

Abstract

We propose a mixed finite element method for Stokes flow with one degree of freedom per element and facet of simplicial grids. The method is derived by considering the vorticity-velocity-pressure formulation and eliminating the vorticity locally through the use of a quadrature rule. The discrete solution is pointwise divergence-free and the method is pressure robust. The theoretically derived convergence rates are confirmed by numerical experiments.