Local Multigrid in H(curl)

• 来源期刊: 计算数学(英文版)
• 关键词: Edge elements Local multigrid Stable multilevel splittings Subspace correc-tion theory Regular decompositions of H(curl Ω) Helmholtz-type decompositions Local mesh refinement
• 年，卷（期）: 2009,（5）
• 页码范围: 573-603
• 页数: 31页
• 语种: 英文
• DOI: 10.4208/jcm.2009.27.5.012

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 correc-tion 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 lo-cal multigrid in a H1(Ω)-context along with local discrete Helmholtz-type decompositions of the edge element space.