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

Abstract

AbstractWe 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.