Isogeometric C 1 mortar method

We present an isogeometric mortar method for the discretization of the biharmonic equation posed on multi-patch domains. We assume only C 0 -conformity at interfaces and employ a mortar approach to weakly enforce C 1 -continuity across patch interfaces. Discrete inf-sup stability is ensured by selecting a Lagrange multiplier space consisting of splines of degree reduced by two compared to the primal space, with increased smoothness or merged elements near vertices. We prove optimal a priori error estimates and confirm the theoretical findings with a series of numerical experiments.