Stochastic numerical analysis with applications in groundwater flow problems

In this project, we study the numerical approximation of (stochastic) differential equations with a groundwater flow application. We concentrate on the specific application of the remediation of contaminated groundwater.

In this concrete setting, we will model appearing flow and diffusion processes using stochastic partial differential equations to help complete the picture made by measurements.With such a model at hand, the main focus of this project is the numerical approximation of time-dependent (stochastic) partial differential equations.

We will work in the field of stochastic numerics which is an intersection between numerical analysis and probability theory.

More concretely, we will push forward state-of-the-art methods such as domain decomposition for stochastic partial differential equations, extend the theory on randomized time-stepping methods for better convergence rates and study randomized operator splitting methods for more efficient implementations.

We will provide a rigorous error analysis for the numerical methods and implement them.The research will be beneficial as a sound model with a good numerical approximation of the solution offers improved predictions for the above-mentioned application.

Moreover, the research will help to establish state-of-the-art numerical methods for stochastic differential equations appearing in the modeling part of the project and extend the theory on modern randomized methods for deterministic equations.