Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Virtual Element Method for Quasilinear Elliptic Problems   We present a Virtual Element Method (VEM) for the solution of Dirichlet
problems for the quasilinear equation $-\text{div} (k(u)\text{grad} u)=f$ with
essential boundary conditions. Within the VEM the nonlinear coefficient is
evaluated with the piecewise polynomial projection of the virtual element
ansatz.
  Well posedness of the discrete problem and optimal order a priori error
estimates in the $H^1$ and $L^2$ norms are proven. In addition, the convergence
of fixed point iterations for the solution of the resulting nonlinear system is
established. Numerical examples confirm the convergence analysis.

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The categories of this paper are: cs
5
The categories of this paper are: gr-qc
12
The categories of this paper are: nucl-th
35
The categories of this paper are: mtrl-th
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The categories of this paper are: q-alg
23
The categories of this paper are: solv-int
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The categories of this paper are: plasm-ph
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The categories of this paper are: q-fin
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The categories of this paper are: eess
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The categories of this paper are: hep-th
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The categories of this paper are: nlin
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The categories of this paper are: patt-sol
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The categories of this paper are: comp-gas
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The categories of this paper are: math-ph
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The categories of this paper are: stat
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The categories of this paper are: nucl-ex