TY - JOUR
T1 - Superconvergence and Asymptotic Expansions for Bilinear Finite Volume Element Approximations
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 2
SP - 408
EP - 423
PY - 2013
DA - 2013/06
SN - 6
DO - http://doi.org/10.4208/nmtma.2013.1127nm
UR - https://global-sci.org/intro/article_detail/nmtma/5911.html
KW - Isoparametric bilinear finite volume element scheme, asymptotic expansion, high accuracy combination formula, superconvergence.
AB - <p style="text-align: justify;">Aiming at the isoparametric bilinear finite
volume element scheme, we initially derive an asymptotic expansion
and a high accuracy &nbsp;combination formula of the derivatives in the
sense of pointwise by employing the energy-embedded method on
uniform grids. Furthermore, we prove that the approximate
derivatives are convergent of order two. Finally, numerical examples
verify the theoretical results.</p>