Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A posteriori error estimates for fully discrete fractional-step
  $\vartheta$-approximations for the heat equation   We derive optimal order a posteriori error estimates for fully discrete
approximations of the initial-boundary value problem for the heat equation. For
the discretization in time we apply the fractional-step $\vartheta$-scheme and
for the discretization in space the finite element method with finite element
spaces that are allowed to change with time. The first optimal order a
posteriori error estimates in $L^\infty(0, T ; L^2({\varOmega}))$ are derived
by applying the reconstruction technique.

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The categories of this paper are: acc-phys
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The categories of this paper are: nucl-th
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The categories of this paper are: cond-mat
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The categories of this paper are: alg-geom
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The categories of this paper are: atom-ph
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The categories of this paper are: solv-int
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The categories of this paper are: ao-sci
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The categories of this paper are: supr-con
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The categories of this paper are: astro-ph
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The categories of this paper are: nucl-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: dg-ga
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The categories of this paper are: physics
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The categories of this paper are: math-ph
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The categories of this paper are: bayes-an