Communications in Mathematical Sciences

Volume 21 (2023)

Number 7

Error estimates of the sav method for the coupled Cahn–Hilliard system in copolymer/homopolymer mixtures

Pages: 1895 – 1916

DOI: https://dx.doi.org/10.4310/CMS.2023.v21.n7.a7

Authors

Jin Huang (Laboratory of Mathematics and Complex Systems (Ministry of Education), School of Mathematical Sciences, Beijing Normal University, Beijing, China)

Guanghua Ji (Laboratory of Mathematics and Complex Systems (Ministry of Education), School of Mathematical Sciences, Beijing Normal University, Beijing, China)

Abstract

In this paper, we consider the fully discrete scheme based on the scalar auxiliary variable (SAV) approach in time and the Fourier spectral method in space, for solving the phase-field model of the blend consisting of AB diblock copolymers and C homopolymers. We establish the error estimates of the numerical scheme rigorously, and show that the fully discrete scheme converges with order $O(\tau^2 + h^m)$, where $\tau$, $h$, and $m$ are the time step, spatial step and regularity of the exact solution, respectively. Finally, some numerical simulation results are presented to demonstrate the theoretical results.

Keywords

soft confinement, copolymer/homopolymer mixtures, error estimates, nonlocal term, SAV approach

2010 Mathematics Subject Classification

35Q35, 65M12, 65N35, 76-xx

Received 23 July 2022

Received revised 9 January 2023

Accepted 20 January 2023

Published 9 October 2023