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A novel adaptive local surface refinement technique based on Locally Refined Non-Uniform Rational B-Splines (LR NURBS) is presented. LR NURBS can model complex geometries exactly and are the rational extension of LR B-splines. The local representation of the parameter space overcomes the drawback of non-existent local refinement in standard NURBS-based isogeometric analysis. For a convenient embedding into general finite element code, the B\'ezier extraction operator for LR NURBS is formulated.doi:10.1007/s00466-017-1455-7 fatcat:b3dkxfr6ujg43lk3iao35lqqum