@Article{AAMM-8-517,
author = {Wang , Jianye and Ma , Rui},
title = {Unified a Priori Error Estimate and a Posteriori Error Estimate of CIP-FEM for Elliptic Equations},
journal = {Advances in Applied Mathematics and Mechanics},
year = {2018},
volume = {8},
number = {4},
pages = {517--535},
abstract = {<p style="text-align: justify;">This paper is devoted to a unified a priori and a posteriori error analysis of
CIP-FEM (continuous interior penalty finite element method) for second-order elliptic
problems. Compared with the classic a priori error analysis in literature, our technique
can easily apply for any type regularity assumption on the exact solution, especially
for the case of lower $H^{1+s}$ weak regularity under consideration, where 0 ≤$s$≤ 1/2.
Because of the penalty term used in the CIP-FEM, Galerkin orthogonality is lost and
Céa Lemma for conforming finite element methods can not be applied immediately
when 0≤$s$≤1/2. To overcome this difficulty, our main idea is introducing an auxiliary $C^1$ finite element space in the analysis of the penalty term. The same tool is also utilized
in the explicit a posteriori error analysis of CIP-FEM.</p>},
issn = {2075-1354},
doi = {https://doi.org/10.4208/aamm.2014.m834},
url = {http://global-sci.org/intro/article_detail/aamm/12101.html}
}