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We present functional-type a posteriori error estimates in isogeometric analysis. These estimates, derived on functional grounds, provide guaranteed and sharp upper bounds of the exact error in the energy norm. Moreover, since these estimates do not contain any unknown/generic constants, they are fully computable, and thus provide quantitative information on the error. By exploiting the properties of non-uniform rational B-splines, we present efficient computation of these error estimates. The numerical realization and the quality of the computed error distribution are addressed. The potential and the limitations of the proposed approach are illustrated using several computational examples. [ABSTRACT FROM AUTHOR]

Abstract: While isogeometric analysis has the potential to close the gap between computer aided design and finite element methods, the underlying structure of NURBS (non-uniform rational B-splines) is a weakness when it comes to local refinement. We propose a hybrid method that combines a globally C 1-continuous, piecewise polynomial finite element basis with rational NURBS-mappings in such a way that an isoparametric setting and exact geometry representation are preserved. We define this basis over T-meshes with a hierarchical structure that allows locally restricted refinement. Combined with a state-of-the-art a posteriori error estimator, we present an adaptive refinement procedure. This concept is successfully demonstrated with the Laplace equation, advection–diffusion problems and linear elasticity problems. [Copyright &y& Elsevier]