Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: High-order mass- and energy-conserving SAV-Gauss collocation finite
  element methods for the nonlinear Schr\"odinger equation   A family of arbitrarily high-order fully discrete space-time finite element
methods are proposed for the nonlinear Schr\"odinger equation based on the
scalar auxiliary variable formulation, which consists of a Gauss collocation
temporal discretization and the finite element spatial discretization. The
proposed methods are proved to be well-posed and conserving both mass and
energy at the discrete level. An error bound of the form $O(h^p+\tau^{k+1})$ in
the $L^\infty(0,T;H^1)$-norm is established, where $h$ and $\tau$ denote the
spatial and temporal mesh sizes, respectively, and $(p,k)$ is the degree of the
space-time finite elements. Numerical experiments are provided to validate the
theoretical results on the convergence rates and conservation properties. The
effectiveness of the proposed methods in preserving the shape of a soliton wave
is also demonstrated by numerical results.

11
The categories of this paper are: hep-lat
12
The categories of this paper are: nucl-th
20
The categories of this paper are: acc-phys
22
The categories of this paper are: chao-dyn
18
The categories of this paper are: econ
27
The categories of this paper are: comp-gas
36
The categories of this paper are: cmp-lg
16
The categories of this paper are: stat
19
The categories of this paper are: eess
8
The categories of this paper are: hep-ex
29
The categories of this paper are: funct-an
37
The categories of this paper are: supr-con
30
The categories of this paper are: q-alg
35
The categories of this paper are: mtrl-th
0
The categories of this paper are: hep-ph
23
The categories of this paper are: solv-int