Numerical approximation of 3D stochastic Navier-Stokes equations

• Applicants: Professor Dr. Dominic Breit; Professor Dr. Olaf Ippisch
• Subject Area: Mathematics
• Term: since 2025
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 563880468

We consider the three-dimensional Navier-Stokes equations subject to stochastic perturbations. We are interested in an implementable scheme for the space-time approximation of the problem. In the lifespan of a strong solution we aim to prove optimal convergence rates for the error between the exact and approximate solution. So far, only very few selective results in this direction are available. We plan to consider different types of noise and to compare them with each other: additive noise, multiplicative noise and transport noise. The latter is motivated on the one-hand by the modelling of phenomena from turbulence, on the other hand it can regularise the problem as shown very recently. In a final work package we aim to verify the theoretical results by numerical simulations. This will be realised via the Monte-Carlo method, where each sample requires the solution of a time-dependent Navier-Stokes problem with simulated input. To conduct these expensive numerical experiments we will parallelly run computations on a cluster.

• DFG Programme: Research Grants