Pressure-robustness for the Stokes equations on anisotropic meshes

TL;DR

This paper discusses pressure-robust discretizations for the Stokes equations on anisotropic meshes, highlighting recent advances and providing new numerical insights into their combined challenges.

Contribution

It revisits previous results on pressure-robustness and anisotropic meshes, offering new numerical examples to deepen understanding of their interaction.

Findings

Pressure-robust methods reduce velocity errors independent of pressure approximation.

Anisotropic mesh grading effectively captures flow features in incompressible flows.

New numerical examples illustrate the combined challenges and solutions for pressure-robustness on anisotropic meshes.

Abstract

Pressure-robustness has been widely studied since the conception of the notion and the introduction of the reconstruction approach for classical mixed methods in [5]. Using discretizations capable of yielding velocity solutions that are independent of the pressure approximation has been recognized as essential, and a large number of recent articles attest to this fact, e.g., [1,6]. Apart from the pressure-robustness aspect, incompressible flows exhibit anisotropic phenomena in the solutions which can be dealt with by using anisotropic mesh grading. The recent publications [3,4] deal with the combination of both challenges. We briefly revisit the results from [4] and provide an insightful new numerical example.