Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Numerical approximation of statistical solutions of the incompressible
  Navier-Stokes Equations   Statistical solutions, which are time-parameterized probability measures on
spaces of square-integrable functions, have been established as a suitable
framework for global solutions of incompressible Navier-Stokes equations (NSE).
We compute numerical approximations of statistical solutions of NSE on
two-dimensional domains with non-periodic boundary conditions and empirically
investigate the convergence of these approximations and their observables. For
the numerical solver, we use Monte Carlo sampling with an H(div)-FEM based
deterministic solver. Our numerical experiments for high Reynolds number
turbulent flows demonstrate that the statistics and observables of the
approximations converge. We also develop a novel algorithm to compute structure
functions on unstructured meshes.

7
The categories of this paper are: hep-th
31
The categories of this paper are: ao-sci
36
The categories of this paper are: cmp-lg
24
The categories of this paper are: dg-ga
33
The categories of this paper are: plasm-ph
30
The categories of this paper are: q-alg
22
The categories of this paper are: chao-dyn
32
The categories of this paper are: atom-ph
35
The categories of this paper are: mtrl-th
14
The categories of this paper are: math-ph
34
The categories of this paper are: chem-ph
12
The categories of this paper are: nucl-th
23
The categories of this paper are: solv-int
8
The categories of this paper are: hep-ex
10
The categories of this paper are: q-bio
29
The categories of this paper are: funct-an