Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Arbitrary Lagrangian--Eulerian finite element method for curved and
  deforming surfaces. I. General theory and application to fluid interfaces   An arbitrary Lagrangian--Eulerian (ALE) finite element method for arbitrarily
curved and deforming two-dimensional materials and interfaces is presented
here. An ALE theory is developed by endowing the surface with a mesh whose
in-plane velocity need not depend on the in-plane material velocity, and can be
specified arbitrarily. A finite element implementation of the theory is
formulated and applied to curved and deforming surfaces with in-plane
incompressible flows. Numerical inf--sup instabilities associated with in-plane
incompressibility are removed by locally projecting the surface tension onto a
discontinuous space of piecewise linear functions. The general isoparametric
finite element method, based on an arbitrary surface parametrization with
curvilinear coordinates, is tested and validated against several numerical
benchmarks. A new physical insight is obtained by applying the ALE developments
to cylindrical fluid films, which are computationally and analytically found to
be stable to non-axisymmetric perturbations, and unstable with respect to
long-wavelength axisymmetric perturbations when their length exceeds their
circumference. A Lagrangian scheme is attained as a special case of the ALE
formulation. Though unable to model fluid films with sustained shear flows, the
Lagrangian scheme is validated by reproducing the cylindrical instability.
However, relative to the ALE results, the Lagrangian simulations are found to
have spatially unresolved regions with few nodes, and thus larger errors.

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The categories of this paper are: dg-ga
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The categories of this paper are: plasm-ph
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The categories of this paper are: solv-int
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The categories of this paper are: nlin
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The categories of this paper are: mtrl-th
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-alg
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The categories of this paper are: chao-dyn
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The categories of this paper are: bayes-an
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The categories of this paper are: q-fin
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The categories of this paper are: supr-con
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The categories of this paper are: cs
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The categories of this paper are: gr-qc
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The categories of this paper are: nucl-ex
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The categories of this paper are: chem-ph
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The categories of this paper are: adap-org