TY - JOUR
T1 - Achieving Superconvergence by One-Dimensional Discontinuous Finite Elements: Weak Galerkin Method
AU - Ye , Xiu
AU - Zhang , Shangyou
JO - East Asian Journal on Applied Mathematics
VL - 3
SP - 590
EP - 598
PY - 2022
DA - 2022/04
SN - 12
DO - http://doi.org/10.4208/eajam.030921.141121 
UR - https://global-sci.org/intro/article_detail/eajam/20408.html
KW - Finite element, weak Galerkin, stabilizer free.
AB - <p style="text-align: justify;">A simple stabilizer free weak Galerkin (SFWG) finite element method for
a one-dimensional second order elliptic problem is introduced. In this method, the weak
function is formed by a discontinuous $k$-th order polynomial with additional unknowns
defined on vertex points, whereas its weak derivative is approximated by a polynomial
of degree $k+1.$ The superconvergence of order two for the SFWG finite element solution
is established. It is shown that the elementwise lifted $P_{k+2}$ solution of the $P_k$ SFWG one
converges at the optimal order. Numerical results confirm the theory.</p>