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This work focuses on the development of a super-penalty strategy based on the$L^2$-projection of suitable coupling terms to achieve $C^1$-continuity betweennon-conforming multi-patch isogeometric Kirchhoff plates. In particular, thechoice of penalty parameters is driven by the underlying perturbed saddle pointproblem from which the Lagrange multipliers are eliminated and is performed toguarantee the optimal accuracy of the method. Moreover, by construction, themethod does not suffer from locking also on very coarse meshes. We demonstratethe applicability of the proposed coupling algorithm to Kirchhoff plates bystudying several benchmark examples discretized by non-conforming meshes. Inall cases, we recover the optimal rates of convergence achievable by B-splineswhere we achieve a substantial gain in accuracy per degree-of-freedom comparedto other choices of the penalty parameters.

A projected super-penalty method for the $C^1$-coupling of multi-patch isogeometric Kirchhoff plates