{"title":"The first-order unconditionally stable projection finite element method for the incompressible vector potential magnetohydrodynamics system","authors":"","doi":"10.1016/j.cnsns.2024.108263","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper, we consider a first-order projection finite element scheme for the three dimensional incompressible magnetohydrodynamics system based on a magnetic vector potential formulation by writing the magnetic induction <span><math><mrow><mi>B</mi><mo>=</mo><mi>curl</mi><mi>A</mi></mrow></math></span>, where <span><math><mi>A</mi></math></span> is a magnetic potential. The main advantage of this projection scheme has two-fold. One is that numerical solutions of velocity field and magnetic induction both satisfy the divergence-free condition in fully discrete level. Another is that the proposed scheme is unconditionally stable for any mesh size and time step size. Under a reasonable regularity assumption, we derive spatial–temporal error estimates of the velocity and magnetic vector potential. Finally, numerical results are displayed to illustrate convergence rates.</p></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":null,"pages":null},"PeriodicalIF":3.4000,"publicationDate":"2024-08-07","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/S1007570424004489","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 consider a first-order projection finite element scheme for the three dimensional incompressible magnetohydrodynamics system based on a magnetic vector potential formulation by writing the magnetic induction , where is a magnetic potential. The main advantage of this projection scheme has two-fold. One is that numerical solutions of velocity field and magnetic induction both satisfy the divergence-free condition in fully discrete level. Another is that the proposed scheme is unconditionally stable for any mesh size and time step size. Under a reasonable regularity assumption, we derive spatial–temporal error estimates of the velocity and magnetic vector potential. Finally, numerical results are displayed to illustrate 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.
The submission of manuscripts with cross-disciplinary approaches in nonlinear science and complexity is particularly encouraged.
Topics of interest:
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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