TY - JOUR
T1 - The Derivative Ultraconvergence for Quadratic Triangular Finite Elements
AU - Zhu , Qiding
AU - Meng , Lingxiong
JO - Journal of Computational Mathematics
VL - 6
SP - 857
EP - 864
PY - 2004
DA - 2004/12
SN - 22
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jcm/10289.html
KW - Ultra-closeness, Superconvergence patch recovery (SPR), Ultraconvergence.
AB - <p style="text-align: justify;">This work concerns the ultraconvergence of quadratic finite element approximations of elliptic boundary value problems. A new, discrete least-squares patch recovery technique is proposed to post-process the solution derivatives. Such recovered derivatives are shown to possess ultraconvergence. The keys in the proof are the asymptotic expansion of the bilinear form for the interpolation error and a &quot;localized&quot; symmetry argument. Numerical results are presented to confirm the analysis.</p>