In this article, we decrease the degree of the polynomials on the boundary of the weak functions and modify the definition of the weak laplacian which are introduced in \cite{BiharmonicSFWG} to use the SFWG method for the biharmonic equation. Then we propose the relevant numerical format and obtain the optimal order of error estimates in $H^2$ and $L^2$ norms. Finally, we confirm the estimates using numerical experiments.

翻译：本文降低了弱函数边界上多项式的次数，并修改了文献\cite{BiharmonicSFWG}中引入的弱拉普拉斯算子定义，以应用SFWG方法求解Biharmonic方程。随后我们提出了相应的数值格式，获得了$H^2$和$L^2$范数下的最优阶误差估计。最后通过数值实验验证了该估计。