Lattice Approximations of Semilinear Stochastic Elliptic Equations with Reflection

TL;DR

This paper investigates lattice-based numerical schemes for approximating reflected stochastic elliptic equations driven by white noise in low-dimensional bounded domains, establishing their convergence.

Contribution

It introduces a lattice approximation scheme for reflected stochastic elliptic equations and proves its convergence, advancing numerical methods for such equations.

Findings

Convergence of the lattice approximation scheme is rigorously established.

The scheme effectively approximates reflected stochastic elliptic equations driven by white noise.

The results apply to domains in dimensions 1, 2, and 3.

Abstract

We study lattice approximations of reflected stochastic elliptic equations driven by white noise on a bounded domain in $\mathbb{R}^d,\ d=1,2,3$. The convergence of the scheme is established.