Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A discontinuous Galerkin method for nonlinear biharmonic Schr\"{o}dinger
  equations   This paper proposes and analyzes a fully discrete scheme that discretizes
space with an ultra-weak local discontinuous Galerkin scheme and time with the
Crank--Nicolson method for the nonlinear biharmonic Schr\"odinger equation. We
first rewrite the problem into a system with a second-order spatial derivative
and then apply the ultra-weak discontinuous Galerkin method to the system. The
proposed scheme is more computationally efficient compared with the local
discontinuous Galerkin method because of fewer auxiliary variables, and
unconditionally stable without any penalty terms; it also preserves the mass
and Hamiltonian conservation that are important properties of the nonlinear
biharmonic Schr\"odinger equation. We also derive optimal L2-error estimates of
the semi-discrete scheme that measure both the solution and the auxiliary
variable with general nonlinear terms. Several numerical studies demonstrate
and support our theoretical findings.

3
The categories of this paper are: physics
16
The categories of this paper are: stat
28
The categories of this paper are: alg-geom
32
The categories of this paper are: atom-ph
36
The categories of this paper are: cmp-lg
33
The categories of this paper are: plasm-ph
13
The categories of this paper are: quant-ph
15
The categories of this paper are: nucl-ex
4
The categories of this paper are: cond-mat
29
The categories of this paper are: funct-an
9
The categories of this paper are: nlin
14
The categories of this paper are: math-ph
19
The categories of this paper are: eess
37
The categories of this paper are: supr-con
27
The categories of this paper are: comp-gas
23
The categories of this paper are: solv-int