TY - JOUR
T1 - Convergence Analysis for the Iterated Defect Correction Scheme of Finite Element Methods on Rectangle Grids
AU - Li , Youai
JO - Journal of Computational Mathematics
VL - 3
SP - 297
EP - 306
PY - 2015
DA - 2015/06
SN - 33
DO - http://doi.org/10.4208/jcm.1501-m4426
UR - https://global-sci.org/intro/article_detail/jcm/9843.html
KW - Petrov-Galerkin method, iterated defect correction scheme, convergence, eigenvalue problem.
AB - <p style="text-align: justify;">This paper develops a new method to analyze convergence of the iterated defect correction scheme of finite element methods on rectangular grids in both two and three dimensions. The main idea is to formulate energy inner products and energy (semi)norms into matrix forms. Then, two constants of two key inequalities involved are min and max eigenvalues of two associated generalized eigenvalue problems, respectively. Local versions on the element level of these two generalized eigenvalue problems are exactly solved to obtain sharp (lower) upper bounds of these two constants. This and some essential observations for iterated solutions establish convergence in 2D and the monotone decreasing property in 3D. For two dimensions the results herein improve those in literature; for three dimensions the results herein are new. Numerical results are presented to examine theoretical results.</p>