@Article{CMR-39-437,
author = {Wu , Haijun and Zheng , Weiying},
title = {Uniform Convergence of Multigrid V-Cycle on Adaptively Refined Finite Element Meshes for Elliptic Problems with Discontinuous Coefficients},
journal = {Communications in Mathematical Research },
year = {2023},
volume = {39},
number = {3},
pages = {437--475},
abstract = {<p style="text-align: justify;">The multigrid V-cycle methods for adaptive finite element discretizations of two-dimensional elliptic problems with discontinuous coefficients are
considered. Under the conditions that the coefficient is quasi-monotone up to
a constant and the meshes are locally refined by using the newest vertex bisection algorithm, some uniform convergence results are proved for the standard
multigrid V-cycle algorithm with Gauss-Seidel relaxations performed only on
new nodes and their immediate neighbours. The multigrid V-cycle algorithm
uses $\mathcal{O}(N)$ operations per iteration and is optimal.</p>},
issn = {2707-8523},
doi = {https://doi.org/10.4208/cmr.2022-0047},
url = {http://global-sci.org/intro/article_detail/cmr/21610.html}
}