Convergence of finite element solutions of stochastic partial integro-differential equations driven by white noise

TL;DR

This paper develops and analyzes a finite element and convolution quadrature method for numerically solving stochastic partial integro-differential equations driven by white noise, proving convergence and supporting results with numerical experiments.

Contribution

It introduces a novel numerical scheme combining finite elements and convolution quadrature for this class of equations and establishes sharp convergence rates.

Findings

Proved sharp-order convergence of the numerical solutions.

Validated theoretical results with numerical experiments.

Demonstrated effectiveness of the method for stochastic equations.

Abstract

Numerical approximation of a stochastic partial integro-differential equation driven by a space- time white noise is studied by truncating a series representation of the noise, with finite element method for spatial discretization and convolution quadrature for time discretization. Sharp-order convergence of the numerical solutions is proved up to a logarithmic factor. Numerical examples are provided to support the theoretical analysis.