Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Discrete gradient methods have an energy conservation law   We show for a variety of classes of conservative PDEs that discrete gradient
methods designed to have a conserved quantity (here called energy) also have a
time-discrete conservation law. The discrete conservation law has the same
conserved density as the continuous conservation law, while its flux is found
by replacing all derivatives of the conserved density appearing in the
continuous flux by discrete gradients.

5
The categories of this paper are: gr-qc
4
The categories of this paper are: cond-mat
26
The categories of this paper are: bayes-an
30
The categories of this paper are: q-alg
17
The categories of this paper are: q-fin
27
The categories of this paper are: comp-gas
29
The categories of this paper are: funct-an
21
The categories of this paper are: adap-org
15
The categories of this paper are: nucl-ex
3
The categories of this paper are: physics
20
The categories of this paper are: acc-phys
28
The categories of this paper are: alg-geom
19
The categories of this paper are: eess
16
The categories of this paper are: stat
34
The categories of this paper are: chem-ph
6
The categories of this paper are: astro-ph