Numerical Analysis of Stabilized Second Order Semi-Implicit Finite Element Methods for the Phase-Field Equations (Advances in Applied Mathematics and Mechanics, 2024)
In this paper, we consider two stabilized second-order semi-implicit finiteelement methods for solving the Allen-Cahn and Cahn-Hilliard equations. Stabilizedsemi-implicit schemes are used for temporal discretization, and the finite elementmethod is used for spatial discretization. It is shown that by adding a single linearterm that is of the same order with the truncation error in time, the proposed methodsare all unconditionally energy stable. Error estimates for the two schemes are also established. Numerical examples are presented to confirm the accuracy, efficiency andstability of the proposed methods.