Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Convergence and Optimality of Adaptive Methods for Poisson's Equation in
  the FEEC Framework   Finite Element Exterior Calculus (FEEC) was developed by Arnold, Falk,
Winther and others over the last decade to exploit the observation that mixed
variational problems can be posed on a Hilbert complex, and Galerkin-type mixed
methods can then be obtained by solving finite-dimensional subcomplex problems.
Chen, Holst, and Xu (Math. Comp. 78 (2009) 35-53) established convergence and
optimality of an adaptive mixed finite element method using Raviart-Thomas or
Brezzi-Douglas-Marini elements for Poisson's equation on contractible domains
in two dimensions, which can be viewed as a boundary problem on the de Rham
complex. Recently Demlow and Hirani (Found. Math. Comput. 14 (2014) 1337-1371)
developed fundamental tools for a posteriori analysis on the de Rham complex.
In this paper, we use tools in FEEC to construct convergence and complexity
results on domains with general topology and spatial dimension. In particular,
we construct a reliable and efficient error estimator and a sharper
quasi-orthogonality result using a novel technique. Without marking for data
oscillation, our adaptive method is a contraction with respect to a total error
incorporating the error estimator and data oscillation.

17
The categories of this paper are: q-fin
24
The categories of this paper are: dg-ga
7
The categories of this paper are: hep-th
13
The categories of this paper are: quant-ph
23
The categories of this paper are: solv-int
14
The categories of this paper are: math-ph
37
The categories of this paper are: supr-con
35
The categories of this paper are: mtrl-th
10
The categories of this paper are: q-bio
28
The categories of this paper are: alg-geom
26
The categories of this paper are: bayes-an
11
The categories of this paper are: hep-lat
32
The categories of this paper are: atom-ph
18
The categories of this paper are: econ
20
The categories of this paper are: acc-phys
0
The categories of this paper are: hep-ph