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 their 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 numbers of the systems of algebraic equations resulting from the extended additive average Schwarz method, corresponding to both coarse spaces, are of the order O(H/h) and independent of jumps in the coefficients, where H and h are the mesh parameters.
翻译:在本文中,我们扩展了添加平均 Schwarz 法,通过迫击炮技术解决二等离子体内及其界面的异差系数的第二等离子体边界值问题,在迫击炮技术中,迫击炮的有限元素离散在不匹配的模外线上。在这种两级方法中,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叶质功能。我们证明,扩展的添加平均 Schwarz 法产生的代数等方程系统的条件数与粗体空间相对应,是O(H/h)的顺序,与系数的跳动无关,H和h是网状参数。