A systematic numerical study on weak Galerkin (WG) finite element method for second order linear parabolic problems is presented by allowing polynomial approximations with various degrees for each local element. Convergence of both semidiscrete and fully discrete WG solutions are established in $L^{\infty}(L^2)$ and $L^{\infty}(H^1)$ norms for a general WG element $({\cal P}_{k}(K),\;{\cal P}_{j}(\partial K),\;\big[{\cal P}_{l}(K)\big]^2)$, where $k\ge 1$, $j\ge 0$ and $l\ge 0$ are arbitrary integers. The fully discrete space-time discretization is based on a first order in time Euler scheme. Our results are intended to extend the numerical analysis of WG methods for elliptic problems [J. Sci. Comput., 74 (2018), 1369-1396] to parabolic problems. Numerical experiments are reported to justify the robustness, reliability and accuracy of the WG finite element method.
翻译：对二阶线性抛物线性问题的微弱加勒金(WG)有限元素方法进行系统的数字研究,方法是允许每个局部元素具有不同程度的多元近似值。半分异和完全独立的WG溶液的趋同以$L ⁇ infty}(L2)$和$L ⁇ infty}(H1)$为一般的WG元素$((cal P ⁇ k})(K),\;xcal P ⁇ j}(部分K)\;\ big[$cal P ⁇ l}(K)\bigh]%2]$,其中1美元、$j\ge 0.00美元和$l\ge 0美元是任意的整数。完全离散的空间离异化以时间顺序第一顺序的Euler计划为基础。我们的结果旨在将工作组处理椭圆性问题的方法的数字分析[J.Sci.Comput., 74 (2018), 1369-139.6] 扩大到parlicoltical 问题。据报告,数字实验证明WG定质要素的稳健、可靠性和精确性方法是合理的。
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