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Volume 5, Issue 4
A Note on the Approximation Properties of the Locally Divergence-Free Finite Elements

Jiangguo Liu & Rachel Cali

Int. J. Numer. Anal. Mod., 5 (2008), pp. 693-703.

Published online: 2008-05

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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.

  • AMS Subject Headings

65M60, 65N30, 76M10

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-5-693, author = {Liu , Jiangguo and Cali , Rachel}, title = {A Note on the Approximation Properties of the Locally Divergence-Free Finite Elements}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2008}, volume = {5}, number = {4}, pages = {693--703}, 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.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/833.html} }
TY - JOUR T1 - A Note on the Approximation Properties of the Locally Divergence-Free Finite Elements AU - Liu , Jiangguo AU - Cali , Rachel JO - International Journal of Numerical Analysis and Modeling VL - 4 SP - 693 EP - 703 PY - 2008 DA - 2008/05 SN - 5 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/833.html KW - approximation property, locally divergence-free (LDF), localized $L_2$-projection, solenoidal. AB -

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.

Liu , Jiangguo and Cali , Rachel. (2008). A Note on the Approximation Properties of the Locally Divergence-Free Finite Elements. International Journal of Numerical Analysis and Modeling. 5 (4). 693-703. doi:
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