Error Estimates Of Semi-implicit Numerical Scheme For A Diffuse Interface Model Of Two-phase Magnetohydrodynamic Flows
Abstract
In this paper, we carry out a rigorous error analysis of the fully discrete semi-implicit numerical scheme proposed in Yang et al. (2019) for the diffuse interface model of two-phase magnetohydrodynamics (MHD) flows with different viscosities and electric conductivities in two and three-dimensional cases. The nonlinear and strong coupled properties and the variable coefficients of the model itself bring the major analytical difficulties in the error estimates. Based on three projection operators, including Stokes projection, Maxwell projection and Ritz projection, we select appropriate test functions, apply the Lipschitz continuous properties of the variable coefficients, and develop the strategies of utilizing intermediate terms to address the major difficulties caused by the model itself. Finally, we establish both the spatial and temporal convergence rates.
Recommended Citation
D. Duan et al., "Error Estimates Of Semi-implicit Numerical Scheme For A Diffuse Interface Model Of Two-phase Magnetohydrodynamic Flows," Journal of Computational and Applied Mathematics, vol. 465, article no. 116580, Elsevier, Sep 2025.
The definitive version is available at https://doi.org/10.1016/j.cam.2025.116580
Department(s)
Mathematics and Statistics
Keywords and Phrases
Diffuse interface model; Error estimates; Fully discrete semi-implicit numerical scheme; Two-phase MHD flows
International Standard Serial Number (ISSN)
0377-0427
Document Type
Article - Journal
Document Version
Citation
File Type
text
Language(s)
English
Rights
© 2025 Elsevier, All rights reserved.
Publication Date
01 Sep 2025
Comments
National Natural Science Foundation of China, Grant 11871038