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Volume 27, Issue 2-3
Hanging Nodes in the Unifying Theory of a Posteriori Finite Element Error Control

C. Carstensen & Jun Hu

J. Comp. Math., 27 (2009), pp. 215-236.

Published online: 2009-04

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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 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.

  • Keywords

A posteriori, A priori, Finite element, Hanging node, Adaptive algorithm.

  • AMS Subject Headings

65N10, 65N15, 35J25.

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-27-215, author = {C. Carstensen and Jun Hu}, title = {Hanging Nodes in the Unifying Theory of a Posteriori Finite Element Error Control}, journal = {Journal of Computational Mathematics}, year = {2009}, volume = {27}, number = {2-3}, pages = {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, $Q_1$, 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.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8569.html} }
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 -

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.

C. Carstensen and Jun Hu. (2009). Hanging Nodes in the Unifying Theory of a Posteriori Finite Element Error Control. Journal of Computational Mathematics. 27 (2-3). 215-236. doi:
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