Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Unconditional superconvergence analysis of a linearized Crank-Nicolson
  Galerkin FEM for generalized Ginzburg-Landau equation   In this paper, a linearized Crank-Nicolson Galerkin finite element method
(FEM) for generalized Ginzburg-Landau equation (GLE) is considered, in which,
the difference method in time and the standard Galerkin FEM are employed. Based
on the linearized Crank-Nicolson difference method in time and the standard
Galerkin finite element method with bilinear element in space, the
time-discrete and space-time discrete systems are both constructed. We focus on
a rigorous analysis and consideration of unconditional superconvergence error
estimates of the discrete schemes. Firstly, by virtue of the temporal error
results, the regularity for the time-discrete system is presented. Secondly,
the classical Ritz projection is used to obtain the spatial error with order
$O(h^2)$ in the sense of $L^2-$norm. Thanks to the relationship between the
Ritz projection and the interpolated projection, the superclose estimate with
order $O(\tau^2 + h^2)$ in the sense of $H^1-$norm is derived. Thirdly, it
follows from the interpolated postprocessing technique that the global
superconvergence result is deduced. Finally, some numerical results are
provided to confirm the theoretical analysis.

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The categories of this paper are: astro-ph
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The categories of this paper are: econ
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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-ex
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The categories of this paper are: hep-th
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The categories of this paper are: math-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: gr-qc
28
The categories of this paper are: alg-geom
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The categories of this paper are: ao-sci
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The categories of this paper are: acc-phys
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The categories of this paper are: cs
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The categories of this paper are: hep-ph
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The categories of this paper are: q-bio
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The categories of this paper are: nlin
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The categories of this paper are: nucl-th