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Piecewise $ \mathbf{H^1}$ functions and vector fields associated with meshes generated by independent refinements


Authors: Susanne C. Brenner and Li-Yeng Sung
Journal: Math. Comp. 84 (2015), 1017-1036
MSC (2010): Primary 65N30
DOI: https://doi.org/10.1090/S0025-5718-2014-02866-4
Published electronically: August 27, 2014
MathSciNet review: 3315498
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Abstract: We consider piecewise $ H^1$ functions and vector fields associated with a class of meshes generated by independent refinements and show that they can be effectively analyzed in terms of the number of refinement levels and the shape regularity of the subdomains that appear in the meshes. We derive Poincaré-Friedrichs inequalities and Korn's inequalities for such meshes and discuss an application to a discontinuous finite element method.


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Additional Information

Susanne C. Brenner
Affiliation: Department of Mathematics and Center for Computation and Technology, Louisiana State University, Baton Rouge, Louisiana 70803
Email: brenner@math.lsu.edu

Li-Yeng Sung
Affiliation: Department of Mathematics and Center for Computation and Technology, Louisiana State University, Baton Rouge, Louisiana 70803
Email: sung@math.lsu.edu

DOI: https://doi.org/10.1090/S0025-5718-2014-02866-4
Keywords: Nonconforming meshes, independent refinements, Poincar\'e-Friedrichs inequalities, Korn's inequalities, weakly over-penalized symmetric interior penalty method
Received by editor(s): October 30, 2012
Received by editor(s) in revised form: August 7, 2013
Published electronically: August 27, 2014
Additional Notes: This work was supported in part by the National Science Foundation under Grant No. DMS-10-16332.
Article copyright: © Copyright 2014 American Mathematical Society