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 - <p style="text-align: justify;">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
$\nabla u$.</p>