(untitled) (Journal of Computational Mathematics, 2018)
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.