@Article{CMR-39-3,
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 = {https://global-sci.com/article/81467/uniform-convergence-of-multigrid-v-cycle-on-adaptively-refined-finite-element-meshes-for-elliptic-problems-with-discontinuous-coefficients}
}