Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An implicitly extended Crank-Nicolson scheme for the heat equation on
  time-dependent domains   We consider a time-stepping scheme of Crank-Nicolson type for the heat
equation on a moving domain in Eulerian coordinates. As the spatial domain
varies between subsequent time steps, an extension of the solution at the
previous time step is required. Following Lehrenfeld \& Olskanskii [ESAIM:
M2AN, 53(2):\,585-614, 2019], we apply an implicit extension based on so-called
ghost-penalty terms. For spatial discretisation, a cut finite element method is
used. We derive a complete a priori error analysis in space and time, which
shows in particular second-order convergence in time under a parabolic CFL
condition. Finally, we present numerical results in two and three space
dimensions that confirm the analytical estimates.

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The categories of this paper are: physics
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The categories of this paper are: nucl-th
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The categories of this paper are: math-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: q-bio
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The categories of this paper are: plasm-ph
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The categories of this paper are: econ
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The categories of this paper are: nlin
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The categories of this paper are: cond-mat
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The categories of this paper are: dg-ga
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The categories of this paper are: adap-org
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The categories of this paper are: chem-ph
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The categories of this paper are: q-alg
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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: comp-gas