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Error Analysis Of A Fully Discrete Projection Method For Magnetohydrodynamic System, Qianqian Ding, Xiaoming He, Xiaonian Long, Shipeng Mao
Error Analysis Of A Fully Discrete Projection Method For Magnetohydrodynamic System, Qianqian Ding, Xiaoming He, Xiaonian Long, Shipeng Mao
Mathematics and Statistics Faculty Research & Creative Works
In this paper, we develop and analyze a finite element projection method for magnetohydrodynamics equations in Lipschitz domain. A fully discrete scheme based on Euler semi-implicit method is proposed, in which continuous elements are used to approximate the Navier–Stokes equations and H(curl) conforming Nédélec edge elements are used to approximate the magnetic equation. One key point of the projection method is to be compatible with two different spaces for calculating velocity, which leads one to obtain the pressure by solving a Poisson equation. The results show that the proposed projection scheme meets a discrete energy stability. In addition, with the …
Error Analysis Of A Fully Discrete Projection Method For Magnetohydrodynamic System, Qianqian Ding, Xiaoming He, Xiaonian Long, Shipeng Mao
Error Analysis Of A Fully Discrete Projection Method For Magnetohydrodynamic System, Qianqian Ding, Xiaoming He, Xiaonian Long, Shipeng Mao
Mathematics and Statistics Faculty Research & Creative Works
In this paper, we develop and analyze a finite element projection method for magnetohydrodynamics equations in Lipschitz domain. A fully discrete scheme based on Euler semi-implicit method is proposed, in which continuous elements are used to approximate the Navier–Stokes equations and H(curl) conforming Nédélec edge elements are used to approximate the magnetic equation. One key point of the projection method is to be compatible with two different spaces for calculating velocity, which leads one to obtain the pressure by solving a Poisson equation. The results show that the proposed projection scheme meets a discrete energy stability. In addition, with the …