Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Probabilistic analysis of the upwind scheme for transport   We provide a probabilistic analysis of the upwind scheme for
multi-dimensional transport equations. We associate a Markov chain with the
numerical scheme and then obtain a backward representation formula of
Kolmogorov type for the numerical solution. We then understand that the error
induced by the scheme is governed by the fluctuations of the Markov chain
around the characteristics of the flow. We show, in various situations, that
the fluctuations are of diffusive type. As a by-product, we prove that the
scheme is of order 1/2 for an initial datum in BV and of order 1/2-a, for all
a>0, for a Lipschitz continuous initial datum. Our analysis provides a new
interpretation of the numerical diffusion phenomenon.

15
The categories of this paper are: nucl-ex
32
The categories of this paper are: atom-ph
30
The categories of this paper are: q-alg
20
The categories of this paper are: acc-phys
21
The categories of this paper are: adap-org
24
The categories of this paper are: dg-ga
14
The categories of this paper are: math-ph
4
The categories of this paper are: cond-mat
1
The categories of this paper are: cs
9
The categories of this paper are: nlin
37
The categories of this paper are: supr-con
35
The categories of this paper are: mtrl-th
7
The categories of this paper are: hep-th
34
The categories of this paper are: chem-ph
22
The categories of this paper are: chao-dyn
25
The categories of this paper are: patt-sol