DFG-funded research projects

Grid adaptation for high-resolution finite element schemes with application to compressible flows

Between 2007-2010 I was researcher in the projects KU 1503/3-1 and KU 1503/3-2 (PI: Dmitri Kuzmin) focussing on the development of rigoros 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-dependen 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.

High-resolution finite element schemes and efficient iterative solver for the numerical simulation of convection-dominated flows

Between 2004-2007 I was researcher in the project KU 1503/1-2 (PI: Dmitri Kuzmin), which focused on the development of positivity-preserving high-resolution finite element schemes for convection-dominated transport problems. The main result of the project is the family of algebraic flux correction (AFC) schemes, which is a novel approach to the design of high-resolution schemes that entirely builds on algebraic design criteria (M-matrix, local extremum diminishing schemes, discrete upwinding) for the construction of positivity-preserving discretizations.