A Note on the Approximation Properties of the Locally Divergence-Free Finite Elements

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Abstract

This paper investigates construction and approximation properties of the locally divergence-free (LDF) finite elements. Numerical stability of the natural and normalized bases for the LDF elements is analyzed. Error estimates about the jumps and the total divergence of the localized $L_2$-projection are proved and validated through numerical examples.

Keywords:

approximation property locally divergence-free (LDF) localized $L_2$-projection solenoidal.
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