Numerical Mathematics and Scientific Computing

The group contributes to the following mathematical research topics of WIAS:

This work is motivated by the needs of the numerical solution of partial differential equations by finite element or finite volume methods. In order to apply these methods, a given domain has to be subdivided into a number of cells with simple geometry. The quality of this subdivision affects the accuracy and convergence of the method. Boundary conforming Delaunay meshes with good quality are the prerequisite for the construction of the Voronoi-box based finite volume method. This method allows to carry over important qualitative properties from the continuous problem to the discretized one. The project is devoted to the construction of boundary conforming Delaunay meshes for three-dimensional domains. [>> more]

The main field of research are schemes for convection-diffusion equations, transport equations with exponential nonlinearities and Navier-Stokes equations (turbulent flows). The methods are based on FEM and FVM spatial discretizations and on implicit temporal discretizations. Considered applications involve population balance systems and Roosbroeck systems. [>> more]

The mathematical description of many scientific and technological problems leads to systems of partial differential equations (PDEs). [>> more]