A stabilizer free weak Galerkin method with implicit [formula omitted]-schemes for fourth order parabolic problems

Abstract

In this study, we solve the fourth-order parabolic problem by combining the implicit θ-schemes in time for θ∈[12,1] 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 θ=1, and a second-order Crank–Nicolson scheme for θ=12. Then, we determine the optimal convergence orders of the error in the H2 and L2 norms after analyzing the well-posedness of the schemes. The theoretical findings are validated by numerical experiments.