Hanging Nodes in the Unifying Theory of a Posteriori Finite Element Error Control
Year: 2009
Journal of Computational Mathematics, Vol. 27 (2009), Iss. 2-3 : pp. 215–236
Abstract
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, Q1, 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2009-JCM-8569
Journal of Computational Mathematics, Vol. 27 (2009), Iss. 2-3 : pp. 215–236
Published online: 2009-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 22
Keywords: A posteriori A priori Finite element Hanging node Adaptive algorithm.