Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Goal-oriented adaptive mesh refinement for non-symmetric functional
  settings   In this article, a new unified duality theory is developed for
Petrov-Galerkin finite element methods. This novel theory is then used to
motivate goal-oriented adaptive mesh refinement strategies for use with
discontinuous Petrov-Galerkin (DPG) methods. The focus of this article is
mainly on broken ultraweak variational formulations of stationary boundary
value problems, however, many of the ideas presented within are general enough
that they be extended to any such well-posed variational formulation. The
proposed goal-oriented adaptive mesh refinement procedures require the
construction of refinement indicators for both a primal problem and a dual
problem. In the DPG context, the primal problem is simply the system of linear
equations coming from a standard DPG method and the dual problem is a similar
system of equations, coming from a new method which is dual to DPG. This new
method has the same coefficient matrix as the associated DPG method but has a
different load. We refer to this new finite element method as a DPG* method. A
thorough analysis of DPG* methods, as stand-alone finite element methods, is
not given here but will be provided in subsequent articles. For DPG methods,
the current theory of a posteriori error estimation is reviewed and the
reliability estimate in [13, Theorem 2.1] is improved on. For DPG* methods,
three different classes of refinement indicators are derived and several
contributions are made towards rigorous a posteriori error estimation. At the
closure of the article, results of numerical experiments with Poisson's
boundary value problem in a three-dimensional domain are provided. These
results clearly demonstrate the utility of the goal-oriented adaptive mesh
refinement strategies for quantities of interest with either interior or
boundary terms.

16
The categories of this paper are: stat
26
The categories of this paper are: bayes-an
15
The categories of this paper are: nucl-ex
5
The categories of this paper are: gr-qc
3
The categories of this paper are: physics
29
The categories of this paper are: funct-an
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The categories of this paper are: supr-con
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The categories of this paper are: atom-ph
23
The categories of this paper are: solv-int
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The categories of this paper are: quant-ph
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The categories of this paper are: chao-dyn
8
The categories of this paper are: hep-ex
0
The categories of this paper are: hep-ph
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The categories of this paper are: nlin
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The categories of this paper are: alg-geom
33
The categories of this paper are: plasm-ph