A stabilizer free weak Galerkin method with implicit $\theta$-schemes for fourth order parabolic problems

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.