Numerical and convergence analysis of the stochastic Lagrangian averaged Navier-Stokes equations?

The primary emphasis of this work is the development of a finite element based space-time discretization for solving the stochastic Lagrangian averaged Navier-Stokes (LANS-alpha) equations of incompressible fluid turbulence with multiplicative random forcing, under nonperiodic boundary conditions within a bounded polygonal (or polyhedral) domain of Rd, d E {2, 3}. The convergence analysis of a fully discretized numerical scheme is investigated and split into two cases according to the spacial scale alpha, namely we first assume alpha to be controlled by the step size of the space discretization so that it vanishes when passing to the limit, then we provide an alternative study when alpha is fixed. A preparatory analysis of uniform estimates in both alpha and discretization parameters is carried out. Starting out from the stochastic LANS-alpha model, we achieve convergence toward the continuous strong solutions of the stochastic Navier-Stokes equations in 2D when alpha vanishes at the limit. Additionally, convergence toward the continuous strong solutions of the stochastic LANS-alpha model is accomplished if alpha is fixed. Neither of the mentioned convergences involves the Skorokhod theorem. (c) 2022 Elsevier B.V. All rights reserved.