Work

Optimal L 2 error estimates of the decoupled, mass and charge-conservative mixed FEM for the two-phase inductionless MHD model

Year: 2025

Type: article

Abstract: This paper considers the optimal L2-norm error estimates of numerical solutions in a decoupled, mass and charge-conservative mixed finite element method (FEM) for the two-phase inductionless MHD model, which consists of the incompressible inductionless MHD (iMHD) problem and the Cahn–Hilliard equations. Firstly, the targeted problem is split into three linear subproblems by treating the nonlinear terms in the explicit and semi-implicit schemes, and the computational size is reduced. Secondly, the unconditional stability of numerical scheme is provided by choosing different test functions and using the embedding theorem and the Cauchy inequalities. Thirdly, the optimal L2 and H1-norms error estimates of numerical solutions are obtained based on the Ritz quasi-projection and Stokes projection. Finally, several numerical results are given to verify the established theoretical findings and show the performance of the considered numerical scheme.

Source: Results in Applied Mathematics

DOI: 10.1016/j.rinam.2025.100662

Authors: Mengdi Du, Qinzheng Xu, Zhengkang He, Tong Zhang

Language: English

Topic: Advanced Numerical Methods in Computational Mathematics

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $1,770

Funders: National Natural Science Foundation of China, Natural Science Foundation of Shandong Province

Awards: G498616023, G5094126662, G5779840617