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

We model incompressible Stokes flows with an adaptive stabilized finite element method, 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.

Automated summary

The study models incompressible Stokes flows using an adaptive stabilized finite element method, solving a discretely stable saddle-point problem for the velocity-pressure pair approximation. It analyzes the accuracy of different discrete velocity-pressure pairs in continuous finite element spaces, and validates the framework's performance with numerical examples.