@Article{IJNAM-3-3,
author = {Jan, Brandts and Yanping, Chen},
title = {Superconvergence of Least-Squares Mixed Finite Elements},
journal = {International Journal of Numerical Analysis and Modeling},
year = {2006},
volume = {3},
number = {3},
pages = {303--310},
abstract = {<p style="text-align: justify;">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.</p>},
issn = {2617-8710},
doi = {https://doi.org/2006-IJNAM-902},
url = {https://global-sci.com/article/83828/superconvergence-of-least-squares-mixed-finite-elements}
}