Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Posteriori Error Estimation for the p-curl Problem   We derive a posteriori error estimates for a semi-discrete finite element
approximation of a nonlinear eddy current problem arising from applied
superconductivity, known as the $p$-curl problem. In particular, we show the
reliability for non-conforming N\'{e}d\'{e}lec elements based on a residual
type argument and a Helmholtz-Weyl decomposition of
$W^p_0(\text{curl};\Omega)$. As a consequence, we are also able to derive an a
posteriori error estimate for a quantity of interest called the AC loss. The
nonlinearity for this form of Maxwell's equation is an analogue of the one
found in the $p$-Laplacian. It is handled without linearizing around the
approximate solution. The non-conformity is dealt by adapting error
decomposition techniques of Carstensen, Hu and Orlando. Geometric
non-conformities also appear because the continuous problem is defined over a
bounded $C^{1,1}$ domain while the discrete problem is formulated over a weaker
polyhedral domain. The semi-discrete formulation studied in this paper is often
encountered in commercial codes and is shown to be well-posed. The paper
concludes with numerical results confirming the reliability of the a posteriori
error estimate.

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The categories of this paper are: cond-mat
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The categories of this paper are: ao-sci
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The categories of this paper are: math-ph
23
The categories of this paper are: solv-int
27
The categories of this paper are: comp-gas
0
The categories of this paper are: hep-ph
29
The categories of this paper are: funct-an
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The categories of this paper are: hep-ex
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The categories of this paper are: hep-lat
35
The categories of this paper are: mtrl-th
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The categories of this paper are: nucl-th
30
The categories of this paper are: q-alg
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The categories of this paper are: dg-ga
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The categories of this paper are: cmp-lg
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The categories of this paper are: astro-ph
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The categories of this paper are: adap-org