Abstract

This paper proposes and analyzes a fully discrete semi-implicit unconditionally energy stable numerical scheme to solve the Cahn-Hilliard Magnetohydrodynamics (Cahn-Hilliard-MHD) model with variable density. The unconditional energy stability and optimal L2 error estimates are established for the fully discrete scheme. Major challenges in error estimation arise from the variable density, the strong nonlinearities, and the multi-physics coupling of the model. Under the mathematical induction framework, the Ritz quasi-projection and the Stokes quasi-projection, proposed in [SIAM J. Numer. Anal., 61(3):1218-1245, 2023], are utilized to avoid the gradient terms of the projection errors. The H−1 superconvergence error estimates of Ritz projection and Ritz quasi-projection reduce the regularity requirement for the finite element space. Two different sets of test functions are also selected to avoid extra estimations of the L2 norm terms. The summation by parts transfers the backward difference quotient operator from the test function to the trial function, avoiding the need for extra estimation of the test function. A numerical experiment is provided to verify the theoretical results.

Department(s)

Mathematics and Statistics

Publication Status

Full Text Access

Keywords and Phrases

Cahn-Hilliard-MHD model; Fully discrete; Optimal L2 error estimates; Quasi-projection; Variable density

International Standard Serial Number (ISSN)

1007-5704

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2026 Elsevier, All rights reserved.

Publication Date

01 Jan 2026

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Included in

Mathematics Commons

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