Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Nested Variational Time Discretization for Parametric Anisotropic
  Willmore Flow   A variational time discretization of anisotropic Willmore flow combined with
a spatial discretization via piecewise affine finite elements is presented.
Here, both the energy and the metric underlying the gradient flow are
anisotropic, which in particular ensures that Wulff shapes are invariant up to
scaling under the gradient flow. In each time step of the gradient flow a
nested optimization problem has to be solved. Thereby, an outer variational
problem reflects the time discretization of the actual Willmore flow and
involves an approximate anisotropic $L^2$-distance between two consecutive time
steps and a fully implicit approximation of the anisotropic Willmore energy.
The anisotropic mean curvature needed to evaluate the energy integrand is
replaced by the time discrete, approximate speed from an inner, fully implicit
variational scheme for anisotropic mean curvature motion. To solve the nested
optimization problem a Newton method for the associated Lagrangian is applied.
Computational results for the evolution of curves underline the robustness of
the new scheme, in particular with respect to large time steps.

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The categories of this paper are: mtrl-th
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The categories of this paper are: nucl-th
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The categories of this paper are: plasm-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: q-alg
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The categories of this paper are: solv-int
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The categories of this paper are: alg-geom
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The categories of this paper are: nlin
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The categories of this paper are: eess
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The categories of this paper are: hep-ex
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-lat
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The categories of this paper are: hep-th
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-ph