Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A convergent Lagrangian discretization for a nonlinear fourth order
  equation   A fully discrete Lagrangian scheme for numerical solution of the nonlinear
fourth order DLSS equation in one space dimension is analyzed. The
discretization is based on the equation's gradient flow structure in the
$L^2$-Wasserstein metric. We prove that the discrete solutions are strictly
positive and mass conserving. Further, they dissipate both the Fisher
information and the logarithmic entropy. Numerical experiments illustrate the
practicability of the scheme. Our main result is a proof of convergence of
fully discrete to weak solutions in the limit of vanishing mesh size.
Convergence is obtained for arbitrary non-negative initial data with finite
entropy, without any CFL type condition. The key ingredient in the proof is a
discretized version of the classical entropy dissipation estimate.

17
The categories of this paper are: q-fin
20
The categories of this paper are: acc-phys
36
The categories of this paper are: cmp-lg
32
The categories of this paper are: atom-ph
14
The categories of this paper are: math-ph
21
The categories of this paper are: adap-org
13
The categories of this paper are: quant-ph
11
The categories of this paper are: hep-lat
31
The categories of this paper are: ao-sci
5
The categories of this paper are: gr-qc
29
The categories of this paper are: funct-an
8
The categories of this paper are: hep-ex
10
The categories of this paper are: q-bio
4
The categories of this paper are: cond-mat
6
The categories of this paper are: astro-ph
3
The categories of this paper are: physics