Optimal error estimates for a fully discrete, highly efficient decoupled scheme for the 2D/3D diffuse interface two-phase MHD flows
Numerical Analysis
2026-03-17 v2 Numerical Analysis
Abstract
In this paper, we derive optimal L2- and H1-norm error estimates for a fully discrete convex-splitting decoupled finite element method (FEM) for the two-phase diffuse interface magnetohydrodynamics (MHD) system. We use the semi-implicit backward Euler scheme in time and employ the standard inf-sup stable Taylor--Hood or Mini elements to discretize the velocity and pressure. Furthermore, we apply a pressure-correction scheme to decouple the velocity from the pressure. The optimal error estimates are obtained via novel Ritz and Stokes quasi-projection techniques. In addition, the unconditional energy stability of the proposed scheme is ensured. Numerical examples are presented to validate the theoretical analysis.
Keywords
Cite
@article{arxiv.2511.14656,
title = {Optimal error estimates for a fully discrete, highly efficient decoupled scheme for the 2D/3D diffuse interface two-phase MHD flows},
author = {Ke Zhang and Haiyan Su},
journal= {arXiv preprint arXiv:2511.14656},
year = {2026}
}