TY - JOUR
T1 - A Posteriori Error Estimation for Non-Conforming Quadrilateral Finite Elements
AU - Ainsworth , Mark
JO - International Journal of Numerical Analysis and Modeling
VL - 1
SP - 1
EP - 18
PY - 2005
DA - 2005/02
SN - 2
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/916.html
KW - a posteriori error estimation, non-conforming finite elements, rotated $\mathbb{Q}_1$ element, non-affine quadrilateral elements.
AB - <p style="text-align: justify;">We derive an a posteriori error estimator giving a
computable upper bound on the error in the energy norm for finite
element approximation using the non-conforming rotated $\mathbb{Q}_1$ finite
element. It is shown that the estimator also gives a local lower bound
up to a generic constant. The bounds do not require additional
assumptions on the regularity of the true solution of the underlying
elliptic problem and, the mesh is only required to be locally
quasi-uniform and may consist of general, non-affine convex
quadrilateral elements.</p>