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Discrete extension operators for mixed finite element spaces on locally refined meshes


Authors: Mark Ainsworth, Johnny Guzmán and Francisco-Javier Sayas
Journal: Math. Comp. 85 (2016), 2639-2650
MSC (2010): Primary 76M10, 65N30, 65N12
DOI: https://doi.org/10.1090/mcom/3074
Published electronically: January 14, 2016
MathSciNet review: 3522965
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Abstract: The existence of uniformly bounded discrete extension operators is established for conforming Raviart-Thomas and Nédelec discretizations of $ H(div)$ and $ H(curl)$ on locally refined partitions of a polyhedral domain into tetrahedra.


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Additional Information

Mark Ainsworth
Affiliation: Divison of Applied Mathematics, Brown University, Providence, Rhode Island 02912
Email: mark_ainsworth@brown.edu

Johnny Guzmán
Affiliation: Division of Applied Mathematics, Brown University, Providence, Rhode Island 02912
Email: johnny_guzman@brown.edu

Francisco-Javier Sayas
Affiliation: Department of Mathematical Sciences, University of Delaware, Newark, Delaware 19716
Email: fjsayas@udel.edu

DOI: https://doi.org/10.1090/mcom/3074
Keywords: Finite elements, Stokes, conforming, divergence-free
Received by editor(s): June 18, 2014
Received by editor(s) in revised form: March 2, 2015, and April 20, 2015
Published electronically: January 14, 2016
Additional Notes: Partial support for the first author under AFOSR contract FA9550-12-1-0399 is gratefully acknowledged
The third author was partially funded by NSF grant DMS 1216356
Article copyright: © Copyright 2016 American Mathematical Society