Recently there has been increased interest in a special class of discretizations for incompressible flows, which produce velocity approximations that are independent of how well the pressure can be approximated. For this reason such methods are called pressure-robust. While classical methods like the family of Taylor-Hood finite elements show a locking phenomenon induced by the viscosity parameter of the fluid, meaning that the error of the discrete velocity solution scales with the inverse of the viscosity, pressure-robust methods do not have this problem. Moreover, incompressible flows tend to form layer structures, for example near walls, and exhibit singularities in the solution near re-entrant edges of the domain. These two effects cause additional difficulties for discretization approaches that can be addressed by anisotropic mesh grading, which uses highly stretched elements in boundary layer regions or near the re-entrant edges. A drawback with regard to anisotropic grading is that only few methods are shown to work for such meshes. The aim of this thesis is to find a combined solution to both challenges, pressure-robustness and anisotropically graded meshes, in order to produce a framework for methods that can satisfy the demands of the two areas. To this effect we use the well known reconstruction approach, that alters classical discretizations in a way that makes them pressure-robust, and connect it with new results from anisotropic interpolation theory to show that a combined approach works. The generated framework is applied to the modified Crouzeix-Raviart and Bernardi-Raugel methods, and the results are supported by a variety of numerical examples.     «

Recently there has been increased interest in a special class of discretizations for incompressible flows, which produce velocity approximations that are independent of how well the pressure can be approximated. For this reason such methods are called pressure-robust. While classical methods like the family of Taylor-Hood finite elements show a locking phenomenon induced by the viscosity parameter of the fluid, meaning that the error of the discrete velocity solution scales with the inverse of t...     »