Research

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].
  
• Making finite elements work on degenerate elements [2024].

Ongoing work