The work of the group "Computational Mathematics" is mainly devoted to
the analysis of modern numerical methods (such as the finite element method
(FEM) and the finite difference method (FDM)) and their applications to
various real-life problems.
We are addressing both classical FEM and FDM issues (convergence,
superconvergence, mesh generation, preservation of qualitative properties
of solutions, etc. with emphasize on high-dimensional problems and
interconnections with discrete and computational geometry) and some recent
trends in numerical analysis, such as reliable a posteriori error
estimates and efficient mesh adaptivity procedures for stationary and
time-dependent problems. In addition, we develop rigorous computational
methods to prove existence of stationary solutions, periodic orbits and
connecting orbits for system of ODEs like the Lorenz system and PDEs like
the Kuramoto-Sivashinsky equation.
In terms of applications and implementation, we are dealing with problems
related to heat conduction, wave propagation, modeling of fuel cells,
computational fluid dynamics, medical image registration and segmentation,
and chaotic dynamical systems.