Convergence Analysis of the Fully Discrete Hybridizable Discontinuous Galerkin Method for the Allen–Cahn Equation Based on the Invariant Energy Quadratization Approach

摘要

Abstract In this paper, we develop a fully discrete scheme to solve the well-known Allen–Cahn equation, where space is discretized by the hybridizable discontinuous Galerkin method, and the time discretization is based on the newly developed Invariant Energy Quadratization approach. At each time step, the scheme results in a linear and uniquely solvable algebraic system. The scheme is shown to be unconditionally energy stable, and the optimal error estimates are rigorously established. Some numerical examples are presented to illustrate the temporal and spatial order of accuracy.