Pressure-robustness for the Stokes equations 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.