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

Abstract

AbstractPressure‐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.