Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A posteriori error analysis for evolution nonlinear Schr\"odinger
  equations up to the critical exponent   We provide a posteriori error estimates in the $L^\infty(L^2)-$norm for
relaxation time discrete and fully discrete schemes for a class of evolution
nonlinear Schr\"odinger equations up to the critical exponent. In particular
for the discretization in time we use the relaxation Crank-Nicolson-type scheme
introduced by Besse in \cite{Besse}. For the discretization in space we use
finite element spaces that are allowed to change between time steps. The
estimates are obtained using the reconstruction technique. Through this
technique the problem is converted to a perturbation of the original partial
differential equation and this makes it possible to use nonlinear stability
arguments as in the continuous problem. In particular, main ingredients we use
in our analysis are the Gagliardo-Nirenberg inequality and the two conservation
laws (mass and energy conservation) of the continuous problem. Numerical
results illustrate that the estimates are indeed of optimal order of
convergence.

17
The categories of this paper are: q-fin
27
The categories of this paper are: comp-gas
15
The categories of this paper are: nucl-ex
35
The categories of this paper are: mtrl-th
19
The categories of this paper are: eess
13
The categories of this paper are: quant-ph
28
The categories of this paper are: alg-geom
7
The categories of this paper are: hep-th
21
The categories of this paper are: adap-org
29
The categories of this paper are: funct-an
34
The categories of this paper are: chem-ph
24
The categories of this paper are: dg-ga
5
The categories of this paper are: gr-qc
22
The categories of this paper are: chao-dyn
20
The categories of this paper are: acc-phys
26
The categories of this paper are: bayes-an