A stabilizer free weak Galerkin method with implicit θ-schemes for fourth order parabolic problems

In this study, we solve the fourth-order parabolic problem by combining the implicit -schemes in time for E E [ 1 2 , 1] with the stabilizer free weak Galerkin (SFWG) method. The semi-discrete and full-discrete numerical schemes are proposed. And specifically, the full-discrete scheme is a first-order backward Euler scheme when = = 1 , and a second-order Crank-Nicolson scheme for = = 1 2 . Then, we determine the optimal convergence orders of the error in the 2 2 and 2 2 norms after analyzing the well-posedness of the schemes. The theoretical findings are validated by numerical experiments.