TY - JOUR
T1 - Uniform Convergence of Multigrid V-Cycle on Adaptively Refined Finite Element Meshes for Elliptic Problems with Discontinuous Coefficients
AU - Wu , Haijun
AU - Zheng , Weiying
JO - Communications in Mathematical Research 
VL - 3
SP - 437
EP - 475
PY - 2023
DA - 2023/04
SN - 39
DO - http://doi.org/10.4208/cmr.2022-0047
UR - https://global-sci.org/intro/article_detail/cmr/21610.html
KW - Multigrid, adaptive finite elements, elliptic problems, discontinuous coefficients, uniform convergence.
AB - <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>