Iterative penalty finite element methods for the steady incompressible magnetohydrodynamic problem

Deng, Jianhua; Tao, Zhen-Zhen; Zhang, Tong

doi:10.1007/s40314-016-0323-y

Cited by 3 publications

(2 citation statements)

References 23 publications

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“…For the discretization approaches of (1.1), a few related contributions include mixed finite elements [15,17,23], discontinuous Galerkin finite elements [?] or iterative penalty finite element methods [12] and so on. The boundary condition under the form P = P 0 + α i on Γ i , i = 1, .…”

Section: Introductionmentioning

confidence: 99%

Regularity results for a model in magnetohydrodynamics with imposed pressure

Poirier¹,

Seloula²

2023

Preprint

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The magnetohydrodynamics (MHD) problem is most often studied in a framework where Dirichlet type boundary conditions on the velocity field is imposed. In this Note, we study the (MHD) system with pressure boundary condition, together with zero tangential trace for the velocity and the magnetic field. In a threedimensional bounded possibly multiply connected domain, we first prove the existence of weak solutions in the Hilbert case, and later, the regularity in W 1,p (Ω) for p ≥ 2 and in W 2,p (Ω) for p ≥ 6/5 using the regularity results for some Stokes and elliptic problems with this type of boundary conditions. Furthermore, under the condition of small data, we obtain the existence and uniqueness of solutions in W 1,p (Ω) for 3/2 < p < 2 by using a fixed-point technique over a linearized (MHD) problem.

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Section: Introductionmentioning

confidence: 99%

Regularity results for a model in magnetohydrodynamics with imposed pressure

Poirier¹,

Seloula²

2023

Preprint

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“…Also in [1,3], the authors have studied the stationary magnetohydrodynamic equations of electrically and heat conducting fluid. For the discretization approaches of (M H D), a few related contributions include mixed finite elements [13,14,16], discontinuous galerkin finite elements [15] or iterative penalty finite element methods [12] and so on. The boundary condition under the form P = P 0 + α i on Γ i , i = 1, .…”

Section: Introductionmentioning

confidence: 99%