@Article{JCM-30-223,
author = {Huangxin Chen, Xuejun Xu and Weiying Zheng},
title = {Local Multilevel Methods for Second-Order Elliptic Problems with Highly Discontinuous Coefficients},
journal = {Journal of Computational Mathematics},
year = {2012},
volume = {30},
number = {3},
pages = {223--248},
abstract = {<p style="text-align: justify;">In this paper, local multiplicative and additive multilevel methods on adaptively refined meshes are considered for second-order elliptic problems with highly discontinuous coefficients. For the multilevel-preconditioned system, we study the distribution of its spectrum by using the abstract Schwarz theory. It is proved that, except for a few small eigenvalues, the spectrum of the preconditioned system is bounded quasi-uniformly with respect to the jumps of the coefficient and the mesh sizes. The convergence rate of multilevel-preconditioned conjugate gradient methods is shown to be quasi-optimal regarding the jumps and the meshes. Numerical experiments are presented to illustrate the theoretical findings.</p>},
issn = {1991-7139},
doi = {https://doi.org/10.4208/jcm.1109-m3401},
url = {http://global-sci.org/intro/article_detail/jcm/8427.html}
}