TY - JOUR
T1 - Unified a Priori Error Estimate and a Posteriori Error Estimate of CIP-FEM for Elliptic Equations
AU - Wang , Jianye
AU - Ma , Rui
JO - Advances in Applied Mathematics and Mechanics
VL - 4
SP - 517
EP - 535
PY - 2018
DA - 2018/05
SN - 8
DO - http://doi.org/10.4208/aamm.2014.m834
UR - https://global-sci.org/intro/article_detail/aamm/12101.html
KW - Finite element methods, continuous interior penalty, priori error estimate, posteriori error analysis.
AB - <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>