TY - JOUR
T1 - A Posteriori Error Estimators for Nonconforming Approximation
AU - Agouzal , Abdellatif
JO - International Journal of Numerical Analysis and Modeling
VL - 1
SP - 77
EP - 85
PY - 2008
DA - 2008/05
SN - 5
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/799.html
KW - nonconforming finite elements, a posteriori error estimators.
AB - <p style="text-align: justify;">In this paper, an alternative approach for constructing an a
posteriori error estimator for non-conforming approximation of scalar
elliptic equation is introduced. The approach is based on the usage of
post-processing conforming finite element approximation of the
non-conforming solution. Then, the compatible a posteriori error
estimator is defined by the local norms of difference between the
nonconforming approximation and conforming post-processing approximation
on the element plus an additional residual term. We prove in general
dimension the efficiency and the reliability of these estimators,
without Helmholtz decomposition of the error, nor regularity assumption
on the solution or the domain, nor saturation assumption. Finally
explicit constants are given, which prove that these estimators are
robust in suitable norms.</p>