The research group was founded on July 1, 2012. It is supported by the Hungarian Academy of Sciences and it is hosted at the Eötvös Loránd University in Budapest. In 2017 the group received support for another 5 years of scientific activity.
The main objective of the group is to provide the theoretical background in numerical mathematics, being extremely important in technical and industrial applications, and to gather scientists
working in this field.
Numerical methods providing approximative solutions to systems of partial differential equations are needed in various fields of science. Our research group investigates elliptic, parabolic, and
hyperbolic problems by applying already existing and new tools as well, such as iterative methods based on preconditioning operators, discontinuous finite element methods, techniques from operator semigroup theory, operator splitting procedures, exponential and Magnus integrators, and Richardson extrapolation. The new methods developed are then implemented to examples modelling real-life phenomena, e.g., air pollution transport models, fuel cell models, Maxwell equations, shallow water equations.
Analysis of evolutionary problems on complex networks play an important role in the work of the research group. Modelling of network processes by systems of differential equations serves as a link to the previous topic. The aim of this line of research is to explore the characteristics obtained from the structure of the network, to ensure the efficient solvability of the equations, and to investigate the reliability of the networks.
Keywords of our research topics:
- convergence analysis of operator splitting procedures
- analysis of strong stability preserving (SSP) methods
- application of exponential and Magnus integrators for nonlinear problems
- efficient numerical treatment of shallow water equations
- study of air pollution transport models
- study of biological models
- simulation of epidemic and information spread on networks
- analysis of differential equations obtained from mean-field approximation
- analysis of network processes on adaptive graphs
- control of network processes by changing the structure of the graph
- preconditioning operators, iterative methods, construction and convergence analysis
- preservation of qualitative properties of elliptic and parabolic PDEs under the discretization
- Richardson extrapolation and its application to real-life problems