AbstractWe investigate the mortar finite element method for second order elliptic boundary value problems on domains which are decomposed into patches $$\Omega _k$$
Ω
k
with tensor-product NURBS parameterizations. We follow the methodology of IsoGeometric Analysis (IGA) and choose discrete spaces $$X_{h,k}$$
X
h
,
k
on each patch $$\Omega _k$$
Ω
k
as tensor-product NURBS spaces of the same or higher degree as given by the parameterization. Our work is an extension of Brivadis et al. (Comput Methods Appl Mech Eng 284:292–319, 2015) and highlights several aspects which did not receive full attention before. In particular, by choosing appropriate spaces of polynomial splines as Lagrange multipliers, we obtain a uniform infsup-inequality. Moreover, we provide a new additional condition on the discrete spaces $$X_{h,k}$$
X
h
,
k
which is required for obtaining optimal convergence rates of the mortar method. Our numerical examples demonstrate that the optimal rate is lost if this condition is neglected.