The research team focuses primarily on the study, design, analysis, and implementation of numerical methods for approximate solutions of boundary and initial-boundary value problems for partial differential equations. Particular attention is paid to the finite volume method, the finite element method, and, in collaboration with a group specializing in geometry, also to isogeometric analysis (including algorithmization and parallelization).
In the field of applications, the team focuses on numerical modelling of viscous compressible and incompressible fluids with an emphasis on water turbines, turbulence modelling, and river flow and flood simulations. The research team also addresses problems involving the minimization of energy functionals (e.g. in the context of solid deformations) using finite element discretization and numerical optimization techniques.