TY - JOUR
T1 - Local Multilevel Method on Adaptively Refined Meshes for Elliptic Problems with Smooth Complex Coefficients
AU - Shishun Li, Xinping Shao & Zhiyong Si
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 3
SP - 336
EP - 355
PY - 2015
DA - 2015/08
SN - 8
DO - http://doi.org/10.4208/nmtma.2015.m1323
UR - https://global-sci.org/intro/article_detail/nmtma/12413.html
KW - 
AB - <p style="text-align: justify;">In this paper, a local multilevel algorithm is investigated for solving linear systems arising from adaptive finite element approximations of second order elliptic problems with smooth complex coefficients. It is shown that the abstract theory for local multilevel algorithm can also be applied to elliptic problems whose dominant coefficient is complex valued. Assuming that the coarsest mesh size is sufficiently small, we prove that this algorithm with Gauss-Seidel smoother is convergent and optimal on the adaptively refined meshes generated by the newest vertex bisection algorithm. Numerical experiments are reported to confirm the theoretical analysis.</p>