@Article{AAMM-17-538,
author = {Gao , Fuzheng and Zhang , Shangyou},
title = {An Explicit Superconvergent Weak Galerkin Finite Element Method for the Heat Equation},
journal = {Advances in Applied Mathematics and Mechanics},
year = {2024},
volume = {17},
number = {2},
pages = {538--553},
abstract = {<p style="text-align: justify;">An explicit two-order superconvergent weak Galerkin finite element
method is designed and analyzed for the heat equation on triangular and tetrahedral grids. For two-order superconvergent $P_k$ weak Galerkin finite elements, the auxiliary inter-element functions must be $P_{k+1}$ polynomials. In order to achieve the superconvergence, the usual $H^1$-stabilizer must be also eliminated. For time-explicit weak
Galerkin method, a time-stabilizer is added, on which the time-derivative of the auxiliary variables can be defined. But for the two-order superconvergent weak Galerkin
finite elements, the time-stabilizer must be very weak, an $H^{−2}$-like inner-product instead of an $L^2$-like inner-product. We show the two-order superconvergence for both
semi-discrete and fully-discrete schemes. Numerical examples are provided.</p>},
issn = {2075-1354},
doi = {https://doi.org/10.4208/aamm.OA-2023-0290},
url = {http://global-sci.org/intro/article_detail/aamm/23733.html}
}