Dongmei Duan , Fuzheng Gao , Jinjin Yang , Xiaoming He
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引用次数: 0
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.
期刊介绍:
The Journal of Computational and Applied Mathematics publishes original papers of high scientific value in all areas of computational and applied mathematics. The main interest of the Journal is in papers that describe and analyze new computational techniques for solving scientific or engineering problems. Also the improved analysis, including the effectiveness and applicability, of existing methods and algorithms is of importance. The computational efficiency (e.g. the convergence, stability, accuracy, ...) should be proved and illustrated by nontrivial numerical examples. Papers describing only variants of existing methods, without adding significant new computational properties are not of interest.
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