Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A modified characteristic finite element method for a fully nonlinear
  formulation of the semigeostrophic flow equations   This paper develops a fully discrete modified characteristic finite element
method for a coupled system consisting of the fully nonlinear Monge-Amp\'ere
equation and a transport equation. The system is the Eulerian formulation in
the dual space for the B. J. Hoskins' semigeostrophic flow equations, which are
widely used in meteorology to model slowly varying flows constrained by
rotation and stratification. To overcome the difficulty caused by the strong
nonlinearity, we first formulate (at the differential level) a vanishing moment
approximation of the semigeostrophic flow equations, a methodology recently
proposed by the authors \cite{Feng1,Feng2}, which involves approximating the
fully nonlinear Monge-Amp\'ere equation by a family of fourth order quasilinear
equations. We then construct a fully discrete modified characteristic finite
element method for the regularized problem. It is shown that under certain mesh
and time stepping constraints, the proposed numerical method converges with an
optimal order rate of convergence. In particular, the obtained error bounds
show explicit dependence on the regularization parameter $\vepsi$. Numerical
tests are also presented to validate the theoretical results and to gauge the
efficiency of the proposed fully discrete modified characteristic finite
element method.

22
The categories of this paper are: chao-dyn
36
The categories of this paper are: cmp-lg
4
The categories of this paper are: cond-mat
25
The categories of this paper are: patt-sol
7
The categories of this paper are: hep-th
33
The categories of this paper are: plasm-ph
10
The categories of this paper are: q-bio
28
The categories of this paper are: alg-geom
15
The categories of this paper are: nucl-ex
1
The categories of this paper are: cs
17
The categories of this paper are: q-fin
23
The categories of this paper are: solv-int
31
The categories of this paper are: ao-sci
29
The categories of this paper are: funct-an
3
The categories of this paper are: physics
6
The categories of this paper are: astro-ph