Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Edge-based nonlinear diffusion for finite element approximations of
  convection-diffusion equations and its relation to algebraic flux-correction
  schemes   For the case of approximation of convection--diffusion equations using
piecewise affine continuous finite elements a new edge-based nonlinear
diffusion operator is proposed that makes the scheme satisfy a discrete maximum
principle. The diffusion operator is shown to be Lipschitz continuous and
linearity preserving. Using these properties we provide a full stability and
error analysis, which, in the diffusion dominated regime, shows existence,
uniqueness and optimal convergence. Then the algebraic flux correction method
is recalled and we show that the present method can be interpreted as an
algebraic flux correction method for a particular definition of the flux
limiters. The performance of the method is illustrated on some numerical test
cases in two space dimensions.

4
The categories of this paper are: cond-mat
22
The categories of this paper are: chao-dyn
3
The categories of this paper are: physics
24
The categories of this paper are: dg-ga
17
The categories of this paper are: q-fin
35
The categories of this paper are: mtrl-th
10
The categories of this paper are: q-bio
36
The categories of this paper are: cmp-lg
0
The categories of this paper are: hep-ph
1
The categories of this paper are: cs
18
The categories of this paper are: econ
19
The categories of this paper are: eess
32
The categories of this paper are: atom-ph
11
The categories of this paper are: hep-lat
34
The categories of this paper are: chem-ph
7
The categories of this paper are: hep-th