Björn Stinner: Finite element approximation of rough PDEs on evolving curves

Speaker
Björn Stinner, University of Warwick

Abstract
(This is joint work with Paola Pozzi, University of Duisburg-Essen) Inspired by applications in cell biology we study parabolic partial differential equations on evolving curves with stochastic source or reaction terms. Solutions typically lack regularity that is required to show optimal convergence rates of established numerical methods, specifically with respect to the dependence on time. We present a novel scheme based on a suitable time-integrated variational version of the stochastic PDE. It uses linear surface finite elements and a semi-implicit time discretisation. Convergence in mean is proved where the rates depend on the regularity of the solution. We also discuss some numerical simulations that underpin the theoretical findings.