We present an isogeometric collocation method for solving the biharmonic equation over planar bilinearly parameterized multi-patch domains. The developed approach is based on the use of the globally $C^4$-smooth isogeometric spline space [25] to approximate the solution of the considered partial differential equation, and proposes as collocation points two different choices, namely on the one hand the Greville points and on the other hand the so-called superconvergent points. Several examples demonstrate the potential of our collocation method for solving the biharmonic equation over planar multi-patch domains, and numerically study the convergence behavior of the two types of collocation points with respect to the $L^2$-norm as well as to equivalents of the $H^s$-seminorms for $1 \leq s \leq 4$.

翻译：我们提出了一种等几何配点法，用于在平面双线性参数化多片域上求解双调和方程。该方法基于全局$C^4$光滑等几何样条空间[25]来逼近所考虑的偏微分方程的解，并提出两种不同的配点方案：即Greville点和所谓的超收敛点。多个算例展示了我们的配点法在平面多片域上求解双调和方程的潜力，并通过$L^2$范数以及$1 \leq s \leq 4$时$H^s$半范数的等价形式，数值研究了这两类配点的收敛行为。