Error estimate of full-discrete numerical scheme with for the nonlocal Allen-Cahn model

英文关键词:Nonlocal Allen-Cahn model  linear  unconditionally energy stable  second-order  error analysis.

中文摘要:

      

英文摘要:

      In this work, we study the error estimates of the fully discrete Fourier pseudo-spectral numerical scheme for solving the nonlocal volume-conserved Allen-Cahn (AC) equation. The time marching method of the numerical scheme is based on the well-known Invariant Energy Quadratization (IEQ) method. We demonstrate that the proposed fully discrete numerical method is uniquely solvable, unconditionally energy stable, and obtain the optimal error estimate of the scheme for both space and time. Additionally, we conduct several numerical tests to verify the theoretical results.