In this paper, we extend the additive average Schwarz method to solve second order elliptic boundary value problems with heterogeneous coefficients inside the subdomains and across subdomain interfaces by the mortar technique, where the mortar finite element discretization is on nonmatching meshes. In this two-level method, we enrich the coarse space in two different ways, i.e., by adding eigenfunctions of two variants of the generalized eigenvalue problems. We prove that the condition number for the system of algebraic equations resulting from the extended additive average Schwarz method, corresponding to both coarse spaces, is of the order O(H/h) and independent of jumps of the coefficients, where H and h are the mesh parameters.

翻译：在本文中,我们推广添加式平均 Schwarz 方法,通过迫击炮技术解决二阶椭圆边界值问题,在子域内和子域界面之间使用迫击炮技术解决异差系数问题,在迫击炮中,迫击炮的限定元素离散在不匹配的中间部分上。在这两种方法中,我们以两种不同的方式丰富粗糙的空间,即增加两种通用电子价值问题变异的元件。我们证明,扩展式添加式平均 Schwarz 方法产生的代数系统条件号,与粗地空间相对应,是O(H/h),独立于系数的跳动,H和h是中位参数。