@Article{EAJAM-12-3,
author = {Ye, Xiu and Zhang, Shangyou},
title = {Achieving Superconvergence by One-Dimensional Discontinuous Finite Elements: Weak Galerkin Method},
journal = {East Asian Journal on Applied Mathematics},
year = {2022},
volume = {12},
number = {3},
pages = {590--598},
abstract = {<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>},
issn = {2079-7370},
doi = {https://doi.org/10.4208/eajam.030921.141121},
url = {https://global-sci.com/article/82482/achieving-superconvergence-by-one-dimensional-discontinuous-finite-elements-weak-galerkin-method}
}