TY - JOUR
T1 - Asymptotic Expansion and Superconvergence for Triangular Linear Finite Element on a Class of Typical Mesh
AU - H. Yu & Y. Huang
JO - International Journal of Numerical Analysis and Modeling
VL - 4
SP - 892
EP - 906
PY - 2012
DA - 2012/09
SN - 9
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/664.html
KW - Finite element, Superconvergence, Asymptotic expansion, Extrapolation, Discrete harmonic extension.
AB - <p style="text-align: justify;">In this paper, we present a new approach to obtain the asymptotic expansion and
superconvergence for the linear element on Union Jack mesh. First, we construct a generalized
interpolation function and its discrete harmonic extension by using the energy embedding method
and the method of separation of variables. Then, we present elaborate estimates for the generalized
interpolation function and the harmonic extension. Finally, the asymptotic expansion,
superconvergence and extrapolation are obtained based on those estimates.</p>