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HANGING NODES IN THE UNIFYING THEORY OF A POSTERIORI FINITE ELEMENT ERROR CONTROL

Carsten Carstensen and Jun Hu
Journal of Computational Mathematics
Vol. 27, No. 2/3 (March 2009), pp. 215-236
Stable URL: http://www.jstor.org/stable/43693503
Page Count: 22
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
HANGING NODES IN THE UNIFYING THEORY OF A POSTERIORI FINITE ELEMENT ERROR CONTROL
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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 twodimensional 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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