TY - JOUR
T1 - A Conforming Discontinuous Galerkin Finite Element Method for Second-Order Parabolic Equation
AU - Huo , Fuchang
AU - Sun , Yuchen
AU - Wu , Jiageng
AU - Zhang , Liyuan
JO - International Journal of Numerical Analysis and Modeling
VL - 3
SP - 432
EP - 458
PY - 2025
DA - 2025/03
SN - 22
DO - http://doi.org/10.4208/ijnam2025-1019
UR - https://global-sci.org/intro/article_detail/ijnam/23888.html
KW - Conforming discontinuous Galerkin finite element method, parabolic equation, weak Galerkin finite element method, optimal order convergence.
AB - <p style="text-align: justify;">The conforming discontinuous Galerkin (CDG) finite element method is an innovative
and effective numerical approach to solve partial differential equations. The CDG method is based
on the weak Galerkin (WG) finite element method, and removes the stabilizer in the numerical
scheme. And the CDG method uses the average of the interior function to replace the value of
the boundary function in the standard WG method. The integration by parts is used to construct
the discrete weak gradient operator in the CDG method. This paper uses the CDG method to
solve the parabolic equation. Firstly, the semi-discrete and full-discrete numerical schemes of the
parabolic equation and the well-posedness of the numerical methods are presented. Then, the
corresponding error equations for both numerical schemes are established, and the optimal order
error estimates of $H^1$ and $L^2$ are provided, respectively. Finally, the numerical results of the CDG
method are verified.</p>