2011/05/05 by Guozhu Yu, Jinchao Xu, Yu, Guozhu +3
Engineering · #65F10 #65N20 #65N30 #Advanced Numerical Methods in Computational Mathematics #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods in engineering
paper · pdf · doi:10.48550/arxiv.1105.1173
openalex publication_date 2011/05/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper is devoted to the multigrid convergence analysis for the linear systems arising from the conforming linear finite element discretization of the second order elliptic equations with anisotropic diffusion. The multigrid convergence behavior is known to strongly depend on whether the discretization grid is aligned or non-aligned with the anisotropic direction and analyses in the paper will be mainly focused on two-level algorithms. For an aligned grid case, a lower bound is given for point-wise smoother which shows deterioration of convergence rate. In both aligned and non-aligned cases we show that for a specially designed block smoother the convergence is uniform with respect to both anisotropy ratio and mesh size in the energy norm. The analysis is complemented with numerical experiments which confirm the theoretical results