Piecewise 𝐇¹ functions and vector fields associated with meshes generated by independent refinements

Brenner, Susanne; Sung, Li-Yeng

doi:10.1090/S0025-5718-2014-02866-4

Piecewise $\mathbf {H^1}$ functions and vector fields associated with meshes generated by independent refinements
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by Susanne C. Brenner and Li-Yeng Sung;

Math. Comp. 84 (2015), 1017-1036

DOI: https://doi.org/10.1090/S0025-5718-2014-02866-4

Published electronically: August 27, 2014

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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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