Error Analysis of Euler Semi-implicit Scheme for the Nonstationary Magneto-hydrodynamics Problem with Temperature Dependent Parameters

• Published in: Journal of scientific computing Vol. 85; no. 2; p. 47
• Main Author: Qiu, Hailong
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.11.2020; Springer Nature B.V
• Subjects: Algorithms; Approximation; Boussinesq equations; Computational Mathematics and Numerical Analysis; Error analysis; Estimates; Fluid flow; Fluid mechanics; Fluid pressure; Heat conductivity; Hypotheses; Incompressible flow; Inequality; Magnetohydrodynamics; Mathematical and Computational Engineering; Mathematical and Computational Physics; Mathematical functions; Mathematics; Mathematics and Statistics; Numerical analysis; Parameters; Reynolds number; Temperature dependence; Theoretical; Velocity; Error estimates; Nonstationary magneto-hydrodynamics equations; Stability; Euler semi-implicit scheme; Generalized Boussinesq problem; Mixed finite element; 76M10; 76W05; 65N30
• ISSN: 0885-7474; 1573-7691
• DOI: 10.1007/s10915-020-01357-z

In this article we consider a fully discrete Euler semi-implicit scheme for the nonstationary electromagnetically and thermally driven flow, which is describing the motion of a nonisothermal incompressible magneto-hydrodyna-mics fluid subject to generalized Boussinesq problem with temperature dependent parameters. A prototypical time-stepping scheme, which is comprised of the Euler semi-implicit discretization in time and conforming mixed finite element approximation in space is studied in detail. We obtain that the proposed scheme is unconditionally stable and derive some optimal error estimates for the fluid velocity, the fluid magnetic and the fluid temperature. Moreover, a suboptimal error estimate for the fluid pressure is proved. Numerical results are provided to verify the theoretical rates of the scheme.