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

Abstract

In this study, we solve the fourth-order parabolic problem by combining the implicit $\theta$-schemes in time for $\theta \in [\frac{1}{2},1]$ 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 $\theta =1$, and a second-order Crank–Nicolson scheme for $\theta =\frac{1}{2}$. Then, we determine the optimal convergence orders of the error in the $H^2$ and $L^2$ norms after analyzing the well-posedness of the schemes. The theoretical findings are validated by numerical experiments.