Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A third order BDF energy stable linear scheme for the no-slope-selection
  thin film model   In this paper we propose and analyze a (temporally) third order accurate
backward differentiation formula (BDF) numerical scheme for the
no-slope-selection (NSS) equation of the epitaxial thin film growth model, with
Fourier pseudo-spectral discretization in space. The surface diffusion term is
treated implicitly, while the nonlinear chemical potential is approximated by a
third order explicit extrapolation formula for the sake of solvability. In
addition, a third order accurate Douglas-Dupont regularization term, in the
form of $-A \Delta t^2 \Delta_N^2 ( u^{n+1} - u^n)$, is added in the numerical
scheme. A careful energy stability estimate, combined with Fourier eigenvalue
analysis, results in the energy stability in a modified version, and a
theoretical justification of the coefficient $A$ becomes available. As a result
of this energy stability analysis, a uniform in time bound of the numerical
energy is obtained. And also, the optimal rate convergence analysis and error
estimate are derived in details, in the $\ell^\infty (0,T; \ell^2) \cap \ell^2
(0,T; H_h^2)$ norm, with the help of a linearized estimate for the nonlinear
error terms. %This convergence estimate is the first such result for a third
order accurate scheme for a gradient flow. Some numerical simulation results
are presented to demonstrate the efficiency of the numerical scheme and the
third order convergence. The long time simulation results for
$\varepsilon=0.02$ (up to $T=3 \times 10^5$) have indicated a logarithm law for
the energy decay, as well as the power laws for growth of the surface roughness
and the mound width. In particular, the power index for the surface roughness
and the mound width growth, created by the third order numerical scheme, is
more accurate than those produced by certain second order energy stable schemes
in the existing literature.

22
The categories of this paper are: chao-dyn
21
The categories of this paper are: adap-org
12
The categories of this paper are: nucl-th
35
The categories of this paper are: mtrl-th
17
The categories of this paper are: q-fin
0
The categories of this paper are: hep-ph
37
The categories of this paper are: supr-con
16
The categories of this paper are: stat
30
The categories of this paper are: q-alg
3
The categories of this paper are: physics
36
The categories of this paper are: cmp-lg
27
The categories of this paper are: comp-gas
15
The categories of this paper are: nucl-ex
20
The categories of this paper are: acc-phys
23
The categories of this paper are: solv-int
33
The categories of this paper are: plasm-ph