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Volume 3, Issue 3
Superconvergence of Tetrahedral Linear Finite Elements

Long Chen

Int. J. Numer. Anal. Mod., 3 (2006), pp. 273-282.

Published online: 2006-03

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  • Abstract

In this paper, we show that the piecewise linear finite element solution $u_h$ and the linear interpolation $u_I$ have superclose gradient for tetrahedral meshes, where most elements are obtained by dividing approximate parallelepiped into six tetrahedra. We then analyze a post-processing gradient recovery scheme, showing that the global $L^2$ projection of $\nabla u_h$ is a superconvergent gradient approximation to $\nabla u$.

  • Keywords

superconvergence, finite element methods, tetrahedral elements, post-processing.

  • AMS Subject Headings

65N30

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-3-273, author = {Chen , Long}, title = {Superconvergence of Tetrahedral Linear Finite Elements}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2006}, volume = {3}, number = {3}, pages = {273--282}, abstract = {

In this paper, we show that the piecewise linear finite element solution $u_h$ and the linear interpolation $u_I$ have superclose gradient for tetrahedral meshes, where most elements are obtained by dividing approximate parallelepiped into six tetrahedra. We then analyze a post-processing gradient recovery scheme, showing that the global $L^2$ projection of $\nabla u_h$ is a superconvergent gradient approximation to $\nabla u$.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/900.html} }
TY - JOUR T1 - Superconvergence of Tetrahedral Linear Finite Elements AU - Chen , Long JO - International Journal of Numerical Analysis and Modeling VL - 3 SP - 273 EP - 282 PY - 2006 DA - 2006/03 SN - 3 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/900.html KW - superconvergence, finite element methods, tetrahedral elements, post-processing. AB -

In this paper, we show that the piecewise linear finite element solution $u_h$ and the linear interpolation $u_I$ have superclose gradient for tetrahedral meshes, where most elements are obtained by dividing approximate parallelepiped into six tetrahedra. We then analyze a post-processing gradient recovery scheme, showing that the global $L^2$ projection of $\nabla u_h$ is a superconvergent gradient approximation to $\nabla u$.

Chen , Long. (2006). Superconvergence of Tetrahedral Linear Finite Elements. International Journal of Numerical Analysis and Modeling. 3 (3). 273-282. doi:
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