Our research team deals with the development of new approaches and methods for problems described by boundary and initial-value problems for linear and nonlinear differential equations. The attention is paid to the (turbulent) compressible and incompressible fluid dynamics (water turbines and their shape optimization), biomechanics (we presently focuse especially on stress-strain analyses of the temporomandibular joint with various defects and its consequent reconstruction e.g. with using of replacements) or particle transport. Finite volume and finite element methods and isogeometric analysis are used to solve these problems (including parallel algorithms and their implementation).