Grid adaptation for high-resolution finite element schemes with application to compressible flows
From 2007 to 2010, I was researcher in the projects KU 1503/3-1 and KU 1503/3-2 (PI: Dmitri Kuzmin) focussing on the development of rigorous a posteriori error estimation and grid adaptation techniques tailored to the specific needs of AFC-type high-resolution finite element methods for convection-dominated transport problems and, in particular, inviscid compressible flows. The main results of the project are a hierarchical grid adaptation strategy that enables the efficient treatment of time-dependent flows on dynamically adaptive unstructured grids and a new approach to goal-oriented error estimation that takes into account the violation of the Galerkin orthogonality property due to the local use of flux correction algorithms.