Simple a posteriori error estimators in adaptive isogeometric analysis

In this article we propose two simple a posteriori error estimators for solving second order elliptic problems using adaptive isogeometric analysis. The idea is based on a Serendipity 1pairing   of discrete approximation spaces Shp,k(M)–Shp+1,k+1(M), where the space Shp+1,k+1(M) is considered as an enrichment of the original basis of Shp,k(M) by means of the kk-refinement, a typical unique feature available in isogeometric analysis. The space Shp+1,k+1(M) is used to obtain a higher order accurate isogeometric finite element approximation and using this approximation we propose two simple a posteriori error estimators. The proposed a posteriori error based adaptive hh-refinement methodology using LR B-splines is tested on classical elliptic benchmark problems. The numerical tests illustrate the optimal convergence rates obtained for the unknown, as well as the effectiveness of the proposed error estimators.