Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Numerical solution for the anisotropic Willmore flow of graphs   The Willmore flow is well known problem from the differential geometry. It
minimizes the Willmore functional defined as integral of the mean-curvature
square over given manifold. For the graph formulation, we derive modification
of the Willmore flow with anisotropic mean curvature. We define the weak
solution and we prove an energy equality. We approximate the solution
numerically by the complementary finite volume method. To show the stability,
we re-formulate the resulting scheme in terms of the finite difference method.
By using simple framework of FDM we show discrete version of the energy
equality. The time discretization is done by the method of lines and the
resulting system of ODEs is solved by the Runge-Kutta-Merson solver with
adaptive integration step. We also show experimental order of convergence as
well as results of the numerical experiments, both for several different
anisotropies.

34
The categories of this paper are: chem-ph
28
The categories of this paper are: alg-geom
0
The categories of this paper are: hep-ph
15
The categories of this paper are: nucl-ex
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The categories of this paper are: patt-sol
29
The categories of this paper are: funct-an
33
The categories of this paper are: plasm-ph
1
The categories of this paper are: cs
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The categories of this paper are: stat
5
The categories of this paper are: gr-qc
18
The categories of this paper are: econ
11
The categories of this paper are: hep-lat
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The categories of this paper are: eess
12
The categories of this paper are: nucl-th
6
The categories of this paper are: astro-ph
21
The categories of this paper are: adap-org