We propose an isogeometric mortar method to fourth order elliptic problems. In particular we are interested in the discretization of the biharmonic equation on $C^0$-conforming multi-patch domains and we exploit the mortar technique to weakly enforce $C^1$-continuity across interfaces. In order to obtain discrete inf-sup stability, a particular choice for the Lagrange multiplier space is needed. Actually, we use as multipliers splines of degree reduced by two, w.r.t. the primal spline space, and with merged elements in the neighbourhood of the corners. In this framework, we are able to show optimal a priori error estimates. We also perform numerical tests that reflect theoretical results.

翻译：针对四阶椭圆问题，本文提出一种等几何mortar方法。我们特别关注双调和方程在$C^0$连续多片域上的离散化，并利用mortar技术弱施加界面间的$C^1$连续性。为获得离散inf-sup稳定性，需要为Lagrange乘子空间选取特定形式。具体而言，我们采用相对于原始样条空间次数降低两次、且在角点附近合并单元的样条作为乘子。在此框架下，我们能够证明最优先验误差估计，并通过数值实验验证理论结果。