Year: 2006
Author: Jan Brandts, Yanping Chen
International Journal of Numerical Analysis and Modeling, Vol. 3 (2006), Iss. 3 : pp. 303–310
Abstract
In this paper we consider superconvergence and supercloseness in the least-squares mixed finite element method for elliptic problems. The supercloseness is with respect to the standard and mixed finite element approximations of the same elliptic problem, and does not depend on the properties of the mesh. As an application, we will derive more precise a priori bounds for the least squares mixed method. The superconvergence may be used to define a posteriori error estimators in the usual way. As a by-product of the analysis, a strengthened Cauchy-Buniakowskii-Schwarz inequality is used to prove the coercivity of the least-squares mixed bilinear form in a straight-forward manner. Using the same inequality, it can moreover be shown that the least-squares mixed finite element linear system of equations can basically be solved with one single iteration step of the Block Jacobi method.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2006-IJNAM-902
International Journal of Numerical Analysis and Modeling, Vol. 3 (2006), Iss. 3 : pp. 303–310
Published online: 2006-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 8
Keywords: least squares mixed elements supercloseness superconvergence.