A lowest-degree strictly conservative finite element scheme for incompressible Stokes problem on general triangulations

TL;DR

This paper introduces a new finite element scheme for the incompressible Stokes problem that is stable, conservative, and works on general triangulations using minimal polynomial degrees.

Contribution

It presents a lowest-degree stable finite element pair with enriched velocity space and constant pressure space for the Stokes problem on arbitrary triangulations.

Findings

Stable and conservative finite element pair for Stokes

Works on general triangulations

Uses minimal polynomial degrees for efficiency

Abstract

In this paper, we propose a finite element pair for incompressible Stokes problem. The pair uses a slightly enriched piecewise linear polynomial space for velocity and piecewise constant space for pressure, and is illustrated to be a lowest-degree conservative stable pair for the Stokes problem on general triangulations.