Research performed by Michal Béreš.
The main aim of the thesis is the study and enhancement of methods for the solution of PDEs with the inclusion of the parameters and uncertainties. I mostly focus on the stochastic Galerkin approach and reduced basis approach to the solution of out-coming systems. I focus mainly on problems arising from geosciences like is flow in porous media and porous media with fractures. Also, I focus on the use of a computed solution that can serve as a very computationally inexpensive surrogate of the original problem and can be used e.g. Bayesian inverse problems.