Project B06
(S)PDEs on time-dependent random domains

Project description

This project aims to develop a theory for (stochastic) partial differential equations ((S)PDEs) on random time-dependent domains, and their numerical analysis. We will focus on regularity results for parabolic PDEs on these domains to enable quasi-Monte Carlo methods for numerical discretization, analyze well-posedness of SPDEs on time-dependent domains, and study SPDEs on less regular random time-dependent domains, such as those evolving with Brownian motion. The project will employ the domain mapping approach, mapping uncertain domains to a reference domain, and explore suitable settings for evolving spaces and mappings. 

Principal Investigators

Ana Durdjevac (FU Berlin)

Claudia Schillings (FU Berlin)

Project members

Max Orteu (FU Berlin)

Publications

Preprints

• Djurdjevac, A., Kaarnioja, V., Orteu, M., Schillings, C., 2025. Quasi-Monte Carlo for Bayesian shape inversion governed by the Poisson problem subject to Gevrey regular domain deformations. https://doi.org/10.48550/ARXIV.2502.14661 

• Djurdjevac, A., Kaarnioja, V., Schillings, C., Zepernick, A.-A., 2025. Uncertainty quantification for stationary and time-dependent PDEs subject to Gevrey regular random domain deformations. https://doi.org/10.48550/ARXIV.2502.12345