Guaranteed and Sharp a Posteriori Error Estimates in Isogeometric Analysis

Abstract

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.