Alexandra ZimmermannDuisburg-Essen
Le 10 oct. 2024
Titre : Convergence analysis of a finite volume scheme for a stochastic Allen-Cahn problem
Résumé :
We address the convergence analysis of a numerical scheme for an Allen- Cahn problem with constraint and with a stochastic external force given by a multiplicative noise of Itô type. The problem is set up in a bounded spatial domain of dimension 2 or 3 and homogeneous Neumann boundary conditions are considered.
We propose a time-space discretization, of semi-implicit Euler-Maruyama type with respect to time and a Two-Point Flux Approximation (TPFA) with re- spect to space for a regularized version of the constrained problem. Under the assumption $\Delta t = O(\varepsilon^2+\theta)$ for a positive $\theta$ on the time parameter $\Delta t$ and the regularization parameter $\varepsilon$ we show the convergence our scheme towards the unique variational solution of the problem.
