Robust a posteriori error analysis of the stochastic Cahn-Hilliard equation with rough noise

TL;DR

This paper develops a robust a posteriori error estimate for a fully discrete adaptive finite element method applied to the stochastic Cahn-Hilliard equation with rough noise, including numerical validation.

Contribution

It introduces a new a posteriori error estimate that remains robust against parameters and proposes an adaptive algorithm for the stochastic Cahn-Hilliard equation.

Findings

The error estimate is robust with respect to interfacial width and noise regularization.

The adaptive algorithm effectively improves solution accuracy.

Numerical simulations confirm the theoretical robustness and efficiency.

Abstract

We derive a posteriori error estimate for a fully discrete adaptive finite element approximation of the stochastic Cahn-Hilliard equation with rough noise. The considered model is derived from the stochastic Cahn-Hilliard equation with additive space-time white noise through suitable spatial regularization of the white noise. The a posteriori estimate is robust with respect to the interfacial width parameter as well as the noise regularization parameter. We propose a practical adaptive algorithm for the considered problem and perform numerical simulations to illustrate the theoretical findings.