Workshop on Numerical Methods and Analysis in CFD - Abstract
Kempf, Volker
Recently there has been increased interest in pressure-robust incompressible flow discretizations, where the velocity error does not depend on the pressure. In this context, the Brezzi-Douglas-Marini finite element is of note, as there are exactly divergence-free H(div)-conforming (hybrid) discontinuous Galerkin methods that use it for the velocity discretization, and the associated interpolation operator can be used as reconstruction operator for classical mixed elements to obtain a pressure-robust method. Well known challenges in the numerical solution of flow problems are boundary layer structures in the solution near walls and singularities near re-entrant edges. Both challenges can be overcome by using local anisotropic mesh grading to improve the approximation, which in turn complicates the error analysis. This talk presents recent and new results concerning anisotropic Brezzi-Douglas-Marini interpolation on simplicial and prismatic meshes and shows some numerical examples.