Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An unfitted finite element method using level set functions for
  extrapolation into deformable diffuse interfaces   We explore a new way to handle flux boundary conditions imposed on level
sets. The proposed approach is a diffuse interface version of the shifted
boundary method (SBM) for continuous Galerkin discretizations of conservation
laws in embedded domains. We impose the interface conditions weakly and
approximate surface integrals by volume integrals. The discretized weak form of
the governing equation has the structure of an immersed boundary finite element
method. That is, integration is performed over a fixed fictitious domain.
Source terms are included to account for interface conditions and extend the
boundary data into the complement of the embedded domain. The calculation of
these extra terms requires (i) construction of an approximate delta function
and (ii) extrapolation of embedded boundary data into quadrature points. We
accomplish these tasks using a level set function, which is given analytically
or evolved numerically. A globally defined averaged gradient of this
approximate signed distance function is used to construct a simple map to the
closest point on the interface. The normal and tangential derivatives of the
numerical solution at that point are calculated using the interface conditions
and/or interpolation on uniform stencils. Similarly to SBM, extrapolation back
to the quadrature points is performed using Taylor expansions. The same
strategy is used to construct ghost penalty functions and extension velocities.
Computations that require extrapolation are restricted to a narrow band around
the interface. Numerical results are presented for elliptic, parabolic, and
hyperbolic test problems, which are specifically designed to assess the error
caused by the numerical treatment of interface conditions on fixed and moving
boundaries in 2D.

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The categories of this paper are: nlin
28
The categories of this paper are: alg-geom
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The categories of this paper are: hep-ex
32
The categories of this paper are: atom-ph
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The categories of this paper are: econ
35
The categories of this paper are: mtrl-th
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The categories of this paper are: patt-sol
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The categories of this paper are: nucl-th
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The categories of this paper are: gr-qc
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The categories of this paper are: solv-int
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The categories of this paper are: quant-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-ph
34
The categories of this paper are: chem-ph
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The categories of this paper are: q-fin
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The categories of this paper are: q-alg