We develop a method for solving elliptic partial differential equations on surfaces described by CAD patches that may have gaps/overlaps. The method is based on hybridization using a three-dimensional mesh that covers the gap/overlap between patches. Thus, the hybrid variable is defined on a three-dimensional mesh, and we need to add appropriate normal stabilization to obtain an accurate solution, which we show can be done by adding a suitable term to the weak form. In practical applications, the hybrid mesh may be conveniently constructed using an octree to efficiently compute the necessary geometric information. We prove error estimates and present several numerical examples illustrating the application of the method to different problems, including a realistic CAD model.

翻译：本文提出一种求解椭圆型偏微分方程的方法，适用于由CAD面片描述且可能存在间隙/重叠的曲面。该方法基于杂交技术，利用覆盖面片间间隙/重叠区域的三维网格实现。具体而言，杂交变量定义在三维网格上，需通过添加适当的法向稳定项来确保解的精度，我们证明可通过在弱形式中引入合适项实现这一目标。在实际应用中，可便捷地采用八叉树构建杂交网格，以高效计算必要的几何信息。我们给出了误差估计，并通过多个数值算例（包括一个真实CAD模型）展示了该方法的应用效果。