Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Finite Element Convergence for the Joule Heating Problem with Mixed
  Boundary Conditions   We prove strong convergence of conforming finite element approximations to
the stationary Joule heating problem with mixed boundary conditions on
Lipschitz domains in three spatial dimensions. We show optimal global
regularity estimates on creased domains and prove a priori and a posteriori
bounds for shape regular meshes.

16
The categories of this paper are: stat
36
The categories of this paper are: cmp-lg
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The categories of this paper are: bayes-an
10
The categories of this paper are: q-bio
4
The categories of this paper are: cond-mat
6
The categories of this paper are: astro-ph
9
The categories of this paper are: nlin
13
The categories of this paper are: quant-ph
18
The categories of this paper are: econ
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The categories of this paper are: alg-geom
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The categories of this paper are: adap-org
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-fin
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The categories of this paper are: patt-sol
11
The categories of this paper are: hep-lat
34
The categories of this paper are: chem-ph