Hanging Nodes in the Unifying Theory of a Posteriori Finite Element Error Control (Journal of Computational Mathematics, 2018)
A unified a posteriori error analysis has been developed in [18, 21–23] to analyze thefinite element error a posteriori under a universal roof. This paper contributes to the finiteelement meshes with hanging nodes which are required for local mesh-refining. The two-dimensional1−irregular triangulations into triangles and parallelograms and their combinationsare considered with conforming and nonconforming finite element methods namedafter or by Courant, $Q_1$, Crouzeix-Raviart, Han, Rannacher-Turek, and others for thePoisson, Stokes and Navier-Lamé equations. The paper provides a unified a priori anda posteriori error analysis for triangulations with hanging nodes of degree ≤ 1 which arefundamental for local mesh refinement in self-adaptive finite element discretisations.