Research

Current research projects

Bayesian inverse problems beyond the Gaussian case

Estimation of model parameters with observed data is an essential part of mathematical modeling and scientific computing. However, parameter estimation poses many fundamental and computational challenges... read more

Advanced numerical methods for stochastic partial differential equations

Partial Differential equations are used to model problems in many applications, e.g. in porous media fluid dynamics. To model heterogeneities in the underlying porous media the equations can contain random fields as coefficients... read more

Uncertainty Quantification with discontinuous random fields

To model phenomena in the natural sciences and/or financial markets, oftentimes (partial) differential equations are utilized.The underlying dynamical system may be subject to uncertainty, for instance parameter and domain uncertainty or... read more

Uncertainties in microstructural data

The behaviour of natural, artificial and tailored materials is governed by underlying parameters, which are subject to specific uncertainties. In many applications, one is interested in the stability and the failure probability... read more

Completed projects

Nowadays due to increasing computational resources and scientific progress, it is possible to take also uncertain knowledge into consideration. This project focuses on computational aspects of uncertainty quantification for non-linear convection dominated problems. Mainly two subjects are investigated: First, the development of efficient numerical methods, and their application on problems with relevance for real world applications. In particular on clarifier–thickener models and subsurface two–phase flow in heterogeneous porous media. Second, theoretical aspects of stochastic perturbed nonlinear hyperbolic problems are considered, such as existence and properties of the solution and convergence of numerical methods. More precisely, the focus is on stochastic Galerkin based discretizations, hyperbolic distributions and data-driven stochastic distributions.

For further information please contact Dr. Ilja Kröker

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