Lattice Approximations of Semilinear Stochastic Elliptic Equations with Reflection
arXiv:1807.11777h-index: 5
Originality Incremental advance
AI Analysis
Provides the first convergence proof for numerical schemes of reflected stochastic elliptic equations, addressing a gap in stochastic PDE theory for practitioners.
The paper proves convergence of lattice approximations for reflected stochastic elliptic equations driven by white noise in dimensions 1-3, establishing a rigorous numerical framework for this class of problems.
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.