Pressure-robust and conforming discretization of the Stokes equations on anisotropic meshes

Abstract: Pressure-robust discretizations for incompressible flows have been in the focus of research for the past years. Many publications construct exactly divergence-free methods or use a reconstruction approach [13] for existing methods like the Crouzeix--Raviart element in order to achieve pressure-robustness. To the best of our knowledge, except for our recent publications [3,4], all those articles impose a condition on the shape-regularity of the mesh, and the two mentioned papers that allow for anisotropic elements use a non-conforming velocity approximation. Based on the classical Bernardi--Raugel element we provide a conforming pressure-robust discretization using the reconstruction approach on anisotropic meshes. Numerical examples support the theory.