Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: 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 R^d , d $\in$ {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.

16
The categories of this paper are: stat
32
The categories of this paper are: atom-ph
8
The categories of this paper are: hep-ex
30
The categories of this paper are: q-alg
14
The categories of this paper are: math-ph
29
The categories of this paper are: funct-an
17
The categories of this paper are: q-fin
5
The categories of this paper are: gr-qc
12
The categories of this paper are: nucl-th
37
The categories of this paper are: supr-con
22
The categories of this paper are: chao-dyn
24
The categories of this paper are: dg-ga
21
The categories of this paper are: adap-org
31
The categories of this paper are: ao-sci
33
The categories of this paper are: plasm-ph
10
The categories of this paper are: q-bio