Discrete maximal regularity of an implicit Euler--Maruyama scheme with non-uniform time discretisation for a class of stochastic partial differential equations
Provides a theoretical regularity result for numerical schemes of stochastic PDEs, which is incremental for the numerical analysis community.
The paper establishes discrete maximal L^2-regularity for an implicit Euler--Maruyama scheme with non-uniform time steps applied to stochastic PDEs, matching the continuous counterpart. This provides a theoretical foundation for numerical analysis of such equations.
An implicit Euler--Maruyama method with non-uniform step-size applied to a class of stochastic partial differential equations is studied. A spectral method is used for the spatial discretization and the truncation of the Wiener process. A discrete analogue of maximal $L^2$-regularity of the scheme and the discretised stochastic convolution is established, which has the same form as their continuous counterpart.