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 employs 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.

翻译：本文提出了一种用于离散化定义在多片区域上的双调和方程的等几何mortar方法。我们仅假设交界面处满足$C^0$-连续性，并采用mortar方法在片间弱强制实施$C^1$-连续性。通过选择拉格朗日乘子空间——该空间由比主空间低两次、且在顶点附近具有更高光滑性或合并单元的样条构成——保证了离散的inf-sup稳定性。我们证明了最优先验误差估计，并通过一系列数值实验验证了理论结果。