Václav Kučera
Charles University Prague, Czech Republic


Main scientific results

  • Robust numerical scheme for low Mach number (10-6) as well as transonic and supersonic compressible flows [2007].
  • Robust numerical scheme for fluid structure interactions using the ALE method [2010].
  • Optimal error estimates for DG applied to a nonlinear convection and nonlinear diffusion problem [2010].
  • Analysis of a space-time DG method for nonlinear convection-diffusion [2011].
  • Simulation of voice formation in human vocal chords [2013].
  • Error estimates uniform w.r.t. diffusion for DG for nonlinear convection-diffusion and purely convective problems [2014].
  • "Nice" triangles cannot be subdivided into "ugly" triangles only. [2015].
  • The circumradius condition (estimate) is a simple scaling of the standard maximum angle condition [2016].
  • Development of a numerical method for cell segmentation based on the level set method [2016].
  • Efficient numerical scheme for a nonlocal hydrodynamic model of flocking dynamics [2018].
  • Generalization of known sufficient conditions for FEM convergence [preprint].
  • Formulation of a necessary condition for FEM convergence, construction of various counterexamples [preprint].
  • Error estimates uniform w.r.t. time for DG for advection-diffusion problems [2019].
  • Proof of consistency with the low Mach incompressible limit for a general class of linearized schemes for the compressible Euler equations [2022].
  • "Nice" tetrahedra cannot be subdivided into "ugly" tetrahedra only [2022].
  • Generalization of Godunov's numerical flux to network junctions [2023].

Ongoing work

Currently I am digressing from my usual field of numerical analysis into the world of 3D fractals and chaotic dynamical systems. This was always a hobby of mine and now thanks to the Neuron fund, I can finally start doing serious reserch. As a preview, here are some POV-Ray pictures of 2D Kleinian limit sets, their trivial extensions into 3D and nontrivial 3D extensions.