Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Crank-Nicolson Galerkin approximations to nonlinear Schr\"odinger
  equations with rough potentials   This paper analyses the numerical solution of a class of non-linear
Schr\"odinger equations by Galerkin finite elements in space and a mass- and
energy conserving variant of the Crank-Nicolson method due to Sanz-Serna in
time. The novel aspects of the analysis are the incorporation of rough,
discontinuous potentials in the context of weak and strong disorder, the
consideration of some general class of non-linearities, and the proof of
convergence with rates in $L^{\infty}(L^2)$ under moderate regularity
assumptions that are compatible with discontinuous potentials. For sufficiently
smooth potentials, the rates are optimal without any coupling condition between
the time step size and the spatial mesh width.

9
The categories of this paper are: nlin
28
The categories of this paper are: alg-geom
24
The categories of this paper are: dg-ga
22
The categories of this paper are: chao-dyn
1
The categories of this paper are: cs
32
The categories of this paper are: atom-ph
27
The categories of this paper are: comp-gas
25
The categories of this paper are: patt-sol
30
The categories of this paper are: q-alg
29
The categories of this paper are: funct-an
12
The categories of this paper are: nucl-th
34
The categories of this paper are: chem-ph
5
The categories of this paper are: gr-qc
20
The categories of this paper are: acc-phys
14
The categories of this paper are: math-ph
35
The categories of this paper are: mtrl-th