Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Stability and Error estimates of the SAV Fourier-spectral method for the
  Phase Field Crystal Equation   We consider fully discrete schemes based on the scalar auxiliary variable
(SAV) approach and stabilized SAV approach in time and the Fourier-spectral
method in space for the phase field crystal (PFC) equation. Unconditionally
energy stability is established for both first- and second-order fully discrete
schemes. In addition to the stability, we also provide a rigorous error
estimate which shows that our second-order in time with Fourier-spectral method
in space converges with order $O(\Delta t^2+N^{-m})$, where $\Delta t$, $N$ and
$m$ are time step size, number of Fourier modes in each direction, and
regularity index in space, respectively. We also present numerical experiments
to verify our theoretical results and demonstrate the robustness and accuracy
of the schemes.

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The categories of this paper are: bayes-an
5
The categories of this paper are: gr-qc
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The categories of this paper are: chao-dyn
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The categories of this paper are: quant-ph
1
The categories of this paper are: cs
17
The categories of this paper are: q-fin
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The categories of this paper are: mtrl-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-th
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The categories of this paper are: hep-ex
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The categories of this paper are: hep-lat
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The categories of this paper are: q-bio
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The categories of this paper are: alg-geom
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The categories of this paper are: solv-int
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The categories of this paper are: atom-ph
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The categories of this paper are: stat