Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Optimal error estimates of a Crank--Nicolson finite element projection
  method for magnetohydrodynamic equations   In this paper, we propose and analyze a fully discrete finite element
projection method for the magnetohydrodynamic (MHD) equations. A modified
Crank--Nicolson method and the Galerkin finite element method are used to
discretize the model in time and space, respectively, and appropriate
semi-implicit treatments are applied to the fluid convection term and two
coupling terms. These semi-implicit approximations result in a linear system
with variable coefficients for which the unique solvability can be proved
theoretically. In addition, we use a second-order decoupling projection method
of the Van Kan type \cite{vankan1986} in the Stokes solver, which computes the
intermediate velocity field based on the gradient of the pressure from the
previous time level, and enforces the incompressibility constraint via the
Helmholtz decomposition of the intermediate velocity field. The energy
stability of the scheme is theoretically proved, in which the decoupled Stokes
solver needs to be analyzed in details. Error estimates are proved in the
discrete $L^\infty(0,T;L^2)$ norm for the proposed decoupled finite element
projection scheme. Numerical examples are provided to illustrate the
theoretical results.

27
The categories of this paper are: comp-gas
37
The categories of this paper are: supr-con
8
The categories of this paper are: hep-ex
32
The categories of this paper are: atom-ph
9
The categories of this paper are: nlin
31
The categories of this paper are: ao-sci
12
The categories of this paper are: nucl-th
36
The categories of this paper are: cmp-lg
35
The categories of this paper are: mtrl-th
7
The categories of this paper are: hep-th
6
The categories of this paper are: astro-ph
10
The categories of this paper are: q-bio
25
The categories of this paper are: patt-sol
20
The categories of this paper are: acc-phys
18
The categories of this paper are: econ
26
The categories of this paper are: bayes-an