An Extrapolated Second Order Backward Difference Time-Stepping Scheme for the Magnetohydrodynamics System. (2nd August 2016)

• Record Type: Journal Article
• Authors: Ravindran, S. S.
• Is Part Of: Numerical functional analysis and optimization. Volume 37:Number 8(2016)
• Page Start: 990
• Page End: 1020
• Publication Date: 2016-08-02
• Subjects: Error estimates -- linear extrapolation -- MHD system -- mixed finite element -- second-order backward difference formula (BDF) -- stability -- non-homogeneous; 76W05 -- 65M12 -- 65M06 -- 65M15 -- 65M60; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2016.1181651
• Languages: English
• ISSNs: 0163-0563

Abstract

ABSTRACT: In this article, we introduce a fully implicit, linearly extrapolated second-order backward difference time-stepping scheme for solving a time dependent non-homogeneous magnetohydrodynamic system for electrically conducting fluids. The extrapolated time-stepping scheme is used for time discretization and the mixed finite element method is used for spatial discretization. We first prove unconditional energetic stability without introducing an undesirable exponential Gronwall constant. Complete error analysis is provided without assuming any stability condition or restrictions on the time-step size. Numerical experiments are presented to confirm the theoretical convergence results and efficiency of the scheme.