Two-sided robust and sharp a posteriori error estimates in isogeometric discretization of elliptic problems

Abstract

We present two-sided a posteriori error estimates for isogeometric discretization of elliptic problems. These estimates, derived on functional grounds, provide robust, guaranteed and sharp two-sided 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. The numerical realization and the quality of the computed error distribution are addressed. The potential of the proposed estimates are illustrated using several computational examples.