Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An equilibrated a posteriori error estimator for arbitrary-order
  N\'ed\'elec elements for magnetostatic problems   We present a novel \textit{a posteriori} error estimator for N\'ed\'elec
elements for magnetostatic problems that is constant-free, i.e. it provides an
upper bound on the error that does not involve a generic constant. The
estimator is based on equilibration of the magnetic field and only involves
small local problems that can be solved in parallel. Such an error estimator is
already available for the lowest-degree N\'ed\'elec element [D. Braess, J.
Sch\"oberl, \textit{Equilibrated residual error estimator for edge elements},
Math. Comp. 77 (2008)] and requires solving local problems on vertex patches.
The novelty of our estimator is that it can be applied to N\'ed\'elec elements
of arbitrary degree. Furthermore, our estimator does not require solving
problems on vertex patches, but instead requires solving problems on only
single elements, single faces, and very small sets of nodes. We prove
reliability and efficiency of the estimator and present several numerical
examples that confirm this.

15
The categories of this paper are: nucl-ex
25
The categories of this paper are: patt-sol
5
The categories of this paper are: gr-qc
29
The categories of this paper are: funct-an
21
The categories of this paper are: adap-org
36
The categories of this paper are: cmp-lg
6
The categories of this paper are: astro-ph
4
The categories of this paper are: cond-mat
34
The categories of this paper are: chem-ph
17
The categories of this paper are: q-fin
35
The categories of this paper are: mtrl-th
22
The categories of this paper are: chao-dyn
27
The categories of this paper are: comp-gas
37
The categories of this paper are: supr-con
33
The categories of this paper are: plasm-ph
30
The categories of this paper are: q-alg