We introduce a discretization/approximation scheme for reflected stochastic partial differential equations driven by space–time white noise through systems of reflecting stochastic differential equations. To establish the convergence of the scheme, we study the existence and uniqueness of solutions of Skorohod-type deterministic systems on time-dependent domains. We also need to establish the convergence of an approximation scheme for deterministic parabolic obstacle problems. Both are of independent interest on their own.
"Lattice approximations of reflected stochastic partial differential equations driven by space–time white noise." Ann. Appl. Probab. 26 (6) 3602 - 3629, December 2016. https://doi.org/10.1214/16-AAP1186