@article {ipa|Adaptive isogeometric methods with hierarchical splines: error estimator and convergence|2015,
	title = {Adaptive isogeometric methods with hierarchical splines: error estimator and convergence},
	year = {2015},
	month = {January},
	pages = {30 p.},
	institution = {CNR-IMATI},
	type = {Working paper},
	address = {Pavia},
	abstract = {<p class="rtejustify">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 rened 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.</p>
},
	keywords = {Numerical schemes},
	url = {http://irs.imati.cnr.it/reports/irs15-01},
	author = {A. Buffa and C. Giannelli}
}
