In this paper we develop a Neumann-Neumann type domain decomposition method for elliptic problems on metric graphs. We describe the iteration in the continuous and discrete setting, reformulate the latter in the abstract additive Schwarz framework and prove its convergence to the finite element solution. We provide an implementation and test it on various examples of interest.

翻译：本文针对度量图上的椭圆型问题，提出了一种Neumann-Neumann型区域分解方法。我们在连续与离散框架下描述了迭代过程，将离散情形重新表述为抽象的加法施瓦茨框架，并证明了其收敛于有限元解。我们给出了具体实现，并在多个感兴趣算例上进行了测试。