中文摘要：

我们考虑 H (卷屈，) 围住的 Lipschitz polyhedra 上的椭圆形的变化问题和他们借助于最低顺序边元素的有限元素 Galerkin discretization。我们假设内在的有四面的网孔被连续本地网孔精炼，由有挂节点的本地一致精炼的任何一个或两断精炼创造了。在这个背景，我们开发一个集中理论为有混合变光滑的所谓的本地 multigrid 修正计划。我们证实它的集中率关于精炼步的数字是一致的。证明在 H 依靠本地 multigrid 的相应结果[1 ]() 与边元素空间的本地分离 Helmholtz 类型分解一起的上下文。[从作者抽象]

英文摘要：

We consider H（curl, Ω）-elliptic variational problems on bounded Lipschitz polyhedra and their finite element Galerkin discretization by means of lowest order edge elements. We assume that the underlying tetrahedral mesh has been created by successive local mesh refinement, either by local uniform refinement with hanging nodes or bisection refinement. In this setting we develop a convergence theory for the the so-called local multigrid correction scheme with hybrid smoothing. We establish that its convergence rate is uniform with respect to the number of refinement steps. The proof relies on corresponding results for local multigrid in a H^1 （Ω）-context along with local discrete Helmholtz-type decompositions of the edge element space.