Local Multigrid in H(curl)
Local Multigrid in H(curl)
复制标题
H(curl) 中的局部多重网格
DOI：
10.4208/jcm.2009.27.5.012
复制
发表时间：
2009-09-01
影响因子：
0.9
通讯作者：
Zheng, Weiying
中科院分区：
文献类型：
--
作者：
Hiptmair, Ralf;Zheng, Weiying
本文考虑有界Lipschitz多面体上的H（curl，Ω）-椭圆变分问题及其用最低阶棱边元的有限元Galerkin离散。我们假设底层四面体网格是通过连续的局部网格细化创建的，无论是通过带有悬挂节点的局部均匀细化还是通过对分细化。在这种情况下，我们开发了一个收敛理论的所谓的本地多重网格校正计划与混合平滑。我们建立了它的收敛速度是均匀的细化步骤的数量。证明依赖于相应的结果，在H-1（欧米茄）的上下文中沿着与本地离散亥姆霍兹型分解的边缘元素空间。
We consider H(curl, Omega)-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(Omega)-context along with local discrete Helmholtz-type decompositions of the edge element space.