Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Frequency-explicit approximability estimates for time-harmonic Maxwell's
  equations   We consider time-harmonic Maxwell's equations set in an heterogeneous medium
with perfectly conducting boundary conditions. Given a divergence-free
right-hand side lying in $L^2$, we provide a frequency-explicit approximability
estimate measuring the difference between the corresponding solution and its
best approximation by high-order N\'ed\'elec finite elements. Such an
approximability estimate is crucial in both the a priori and a posteriori error
analysis of finite element discretizations of Maxwell's equations, but the
derivation is not trivial. Indeed, it is hard to take advantage of high-order
polynomials given that the right-hand side only exhibits $L^2$ regularity. We
proceed in line with previously obtained results for the simpler setting of the
scalar Helmholtz equation, and propose a regularity splitting of the solution.
In turn, this splitting yields sharp approximability estimates generalizing
known results for the scalar Helmoltz equation and showing the interest of
high-order methods.

30
The categories of this paper are: q-alg
23
The categories of this paper are: solv-int
24
The categories of this paper are: dg-ga
26
The categories of this paper are: bayes-an
15
The categories of this paper are: nucl-ex
0
The categories of this paper are: hep-ph
16
The categories of this paper are: stat
33
The categories of this paper are: plasm-ph
3
The categories of this paper are: physics
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The categories of this paper are: comp-gas
13
The categories of this paper are: quant-ph
21
The categories of this paper are: adap-org
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The categories of this paper are: cmp-lg
18
The categories of this paper are: econ
17
The categories of this paper are: q-fin
31
The categories of this paper are: ao-sci