Superconvergence of Least-Squares Mixed Finite Elements

Superconvergence of Least-Squares Mixed Finite Elements

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.

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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.

Author Details

Jan Brandts

Yanping Chen