TY - JOUR
T1 - Some New Local Error Estimates in Negative Norms with an Application to Local a Posteriori Error Estimation
AU - Schatz , Alfred H.
JO - International Journal of Numerical Analysis and Modeling
VL - 3
SP - 371
EP - 376
PY - 2006
DA - 2006/03
SN - 3
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/908.html
KW - superconvergence, error estimate, a posteriori.
AB - <p style="text-align: justify;">Here we survey some previously published results and
announce some that have been newly obtained. We first review some of the
results in [3] on estimates for the finite element error at a point.
These estimates and analogous ones in [4] and [7] have been applied to
problems in a posteriori estimates [2], [8], superconvergence [5] and
others [9], [10]. We then discuss the extension of these estimates to
local estimates in $L_∞$ based negative norms. These estimates have been
newly obtained and are applied to the problem of obtaining an
asymptotically exact a posteriori estimator for the maximum norm of the
solution error on each element.</p>