TY - JOUR
T1 - An Error Analysis Method SPP-BEAM and a Construction Guideline of Nonconforming Finite Elements for Fourth Order Elliptic Problems
AU - Hu , Jun
AU - Zhang , Shangyou
JO - Journal of Computational Mathematics
VL - 1
SP - 195
EP - 222
PY - 2020
DA - 2020/02
SN - 38
DO - http://doi.org/10.4208/jcm.1811-m2018-0162
UR - https://global-sci.org/intro/article_detail/jcm/13691.html
KW - Nonconforming finite element, A priori error analysis, Biharmonic equation.
AB - <p style="text-align: justify;">Under two hypotheses of nonconforming finite elements of fourth order elliptic problems, we present a side–patchwise projection based error analysis method (SPP–BEAM for short). Such a method is able to avoid both the regularity condition of exact solutions in the classical error analysis method and the complicated bubble function technique in the recent medius error analysis method. In addition, it is universal enough to admit generalizations. Then, we propose a sufficient condition for these hypotheses by imposing a set of in some sense necessary degrees of freedom of the shape function spaces. As an application, we use the theory to design a $P_3$ second order triangular $H^2$ non-conforming element by enriching two $P_4$ bubble functions and, another $P_4$ second order triangular $H^2$ nonconforming finite element, and a $P_3$ second order tetrahedral $H^2$ non-conforming element by enriching eight $P_4$&nbsp;bubble functions, adding some more degrees of freedom.</p>