{"title":"Optimal convergent analysis of a linearized Euler finite element scheme for the 2D incompressible temperature-dependent MHD-Boussinesq equations","authors":"Shuheng Wang, Yuan Li","doi":"10.1016/j.cnsns.2024.108264","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper, we study a first-order Euler semi-implicit finite element scheme for the two-dimensional incompressible Boussinesq equations for magnetohydrodynamics convection with the temperature-dependent viscosity, electrical conductivity and thermal diffusivity. In finite element discretizations, the mini finite element is used to approximate the velocity and pressure, and the piecewise linear finite element is used to approximate the magnetic field and temperature. The unconditional stability of the proposed scheme is proved. By introducing three projection operators with variable coefficients and using the method of mathematical induction, we obtain optimal error estimates under a CFL type condition. Finally, numerical examples are provided to demonstrate these convergence rates.</p></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":null,"pages":null},"PeriodicalIF":3.4000,"publicationDate":"2024-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Communications in Nonlinear Science and Numerical Simulation","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S1007570424004490","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
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Abstract
In this paper, we study a first-order Euler semi-implicit finite element scheme for the two-dimensional incompressible Boussinesq equations for magnetohydrodynamics convection with the temperature-dependent viscosity, electrical conductivity and thermal diffusivity. In finite element discretizations, the mini finite element is used to approximate the velocity and pressure, and the piecewise linear finite element is used to approximate the magnetic field and temperature. The unconditional stability of the proposed scheme is proved. By introducing three projection operators with variable coefficients and using the method of mathematical induction, we obtain optimal error estimates under a CFL type condition. Finally, numerical examples are provided to demonstrate these convergence rates.
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The journal publishes original research findings on experimental observation, mathematical modeling, theoretical analysis and numerical simulation, for more accurate description, better prediction or novel application, of nonlinear phenomena in science and engineering. It offers a venue for researchers to make rapid exchange of ideas and techniques in nonlinear science and complexity.
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Nonlinear differential or delay equations, Lie group analysis and asymptotic methods, Discontinuous systems, Fractals, Fractional calculus and dynamics, Nonlinear effects in quantum mechanics, Nonlinear stochastic processes, Experimental nonlinear science, Time-series and signal analysis, Computational methods and simulations in nonlinear science and engineering, Control of dynamical systems, Synchronization, Lyapunov analysis, High-dimensional chaos and turbulence, Chaos in Hamiltonian systems, Integrable systems and solitons, Collective behavior in many-body systems, Biological physics and networks, Nonlinear mechanical systems, Complex systems and complexity.
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