Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Adaptive isogeometric methods with hierarchical splines: error estimator
  and convergence   The problem of developing an adaptive isogeometric method (AIGM) for solving
elliptic second-order partial differential equations with truncated
hierarchical B-splines of arbitrary degree and different order of continuity is
addressed. The adaptivity analysis holds in any space dimensions. We consider a
simple residual-type error estimator for which we provide a posteriori upper
and lower bound in terms of local error indicators, taking also into account
the critical role of oscillations as in a standard adaptive finite element
setting. The error estimates are properly combined with a simple marking
strategy to define a sequence of admissible locally refined meshes and
corresponding approximate solutions. The design of a refine module that
preserves the admissibility of the hierarchical mesh configuration between two
consectutive steps of the adaptive loop is presented. The contraction property
of the quasi-error, given by the sum of the energy error and the scaled error
estimator, leads to the convergence proof of the AIGM.

13
The categories of this paper are: quant-ph
23
The categories of this paper are: solv-int
9
The categories of this paper are: nlin
14
The categories of this paper are: math-ph
17
The categories of this paper are: q-fin
18
The categories of this paper are: econ
26
The categories of this paper are: bayes-an
31
The categories of this paper are: ao-sci
7
The categories of this paper are: hep-th
36
The categories of this paper are: cmp-lg
1
The categories of this paper are: cs
27
The categories of this paper are: comp-gas
21
The categories of this paper are: adap-org
12
The categories of this paper are: nucl-th
28
The categories of this paper are: alg-geom
16
The categories of this paper are: stat