A surface finite element scheme for a stochastic PDE on an evolving curve
Numerical Analysis
2025-07-03 v1 Numerical Analysis
Abstract
In this paper we consider an ESFEM method for the advection and diffusion of a scalar quantity on a moving closed curve. The diffusion process is controlled by a forcing term that may include a rough term (specifically a stochastic noise) which in particular destroys the classical time differentiability properties of the solution. We provide a suitable variational solution concept and a fully discrete FEM discretization. Our error analysis appropriately generalizes classical estimates to this weaker setting. We present some numerical simulations that confirm our theoretical findings.
Keywords
Cite
@article{arxiv.2507.01527,
title = {A surface finite element scheme for a stochastic PDE on an evolving curve},
author = {Paola Pozzi and Björn Stinner},
journal= {arXiv preprint arXiv:2507.01527},
year = {2025}
}