TY - JOUR
T1 - Hanging Nodes in the Unifying Theory of a Posteriori Finite Element Error Control
AU - C. Carstensen & Jun Hu
JO - Journal of Computational Mathematics
VL - 2-3
SP - 215
EP - 236
PY - 2009
DA - 2009/04
SN - 27
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jcm/8569.html
KW - A posteriori, A priori, Finite element, Hanging node, Adaptive algorithm.
AB - <p style="text-align: justify;">A unified a posteriori error analysis has been developed in [18, 21–23] to analyze the
finite element error a posteriori under a universal roof. This paper contributes to the finite
element meshes with hanging nodes which are required for local mesh-refining. The two-dimensional
1−irregular triangulations into triangles and parallelograms and their combinations
are considered with conforming and nonconforming finite element methods named
after or by Courant, $Q_1$, Crouzeix-Raviart, Han, Rannacher-Turek, and others for the
Poisson, Stokes and Navier-Lamé equations. The paper provides a unified a priori and
a posteriori error analysis for triangulations with hanging nodes of degree ≤ 1 which are
fundamental for local mesh refinement in self-adaptive finite element discretisations.</p>