Abstract
AbstractIn this article, we consider a weak Galerkin finite element method and a nonuniform two‐step backward differentiation formula scheme for solving the Allen–Cahn equation. A discrete weak gradient operator on discontinuous piecewise polynomials is used in the numerical scheme. It is well‐known that the Allen–Cahn equations have a nonlinear stability property, that is, the free‐energy functional decreases with respect to time. A corresponding energy stability analysis of the discretized system is developed. Optimal order of L2‐norm error estimates are derived. Numerical experiments are preformed to support the theoretical results.
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