Stabilized and Reliable Numerical Scheme for a fully Discrete Allen-Cahn Equation on a Smooth Domain

摘要

The numerical stability and error estimates are some of the well-known studies carried out on a number of commonly used numerical schemes for the Allen-Cahn equation. We exploit these techniques and design a fully discrete scheme consisting of coupling the stabilized Non-standard finite difference in the time and finite element in the space variable. We derived the error estimate in the L~2-norm and proceed to show the unconditional energy stability of the aforementioned scheme. Furthermore, we show that this scheme replicates the properties of the exact solution. Some numerical experiments are performed to support our theoretical analysis.