In this paper, we combine the stabilizer free weak Galerkin (SFWG) method and the implicit $\theta$-schemes in time for $\theta\in [\frac{1}{2},1]$ to solve the fourth-order parabolic problem. In particular, when $\theta =1$, the full-discrete scheme is first-order backward Euler and the scheme is second-order Crank Nicolson scheme if $\theta =\frac{1}{2}$. Next, we analyze the well-posedness of the schemes and deduce the optimal convergence orders of the error in the $H^2$ and $L^2$ norms. Finally, numerical examples confirm the theoretical results.

翻译：本文结合无稳定子弱Galerkin（SFWG）方法与时间方向上的隐式$\theta$-格式（$\theta\in [\frac{1}{2},1]$），求解四阶抛物问题。特别地，当$\theta =1$时，全离散格式为一阶向后欧拉格式；当$\theta =\frac{1}{2}$时，该格式为二阶Crank-Nicolson格式。随后，我们分析格式的适定性，并推导$H^2$和$L^2$范数下误差的最优收敛阶。最后，数值算例验证了理论结果。