Incompressible flow modeling using an adaptive stabilized finite element method based on residual minimization

TL;DR

This paper introduces an adaptive stabilized finite element method for modeling incompressible flows, utilizing residual minimization to improve accuracy and provide robust error estimation for mesh adaptivity.

Contribution

It presents a novel residual minimization-based stabilized finite element approach that effectively handles saddle-point problems in incompressible flow modeling.

Findings

The method accurately models Stokes flows with adaptive mesh refinement.

The saddle-point formulation provides reliable error estimates.

Numerical examples validate the framework's effectiveness.

Abstract

We model incompressible flows with an adaptive stabilized finite element method Stokes flows, which solves a discretely stable saddle-point problem to approximate the velocity-pressure pair. Additionally, this saddle-point problem delivers a robust error estimator to guide mesh adaptivity. We analyze the accuracy of different discrete velocity-pressure pairs of continuous finite element spaces, which do not necessarily satisfy the discrete inf-sup condition. We validate the framework's performance with numerical examples.