Convergence analysis of a conservative finite element scheme for the thermally coupled incompressible inductionless MHD problem

DOI10.1016/j.apnum.2022.07.020zbMath1500.65064OpenAlexW4292166943WikidataQ114208005 ScholiaQ114208005MaRDI QIDQ2085656

Qianqian Ding, Xiaonian Long

Publication date: 18 October 2022

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.apnum.2022.07.020

zbMATH Keywords

mixed finite element methodcharge conservationinductionless MHDdivergence conforming elements

Mathematics Subject Classification ID

Finite difference methods applied to problems in fluid mechanics (76M20) PDEs in connection with biology, chemistry and other natural sciences (35Q92) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Finite element methods applied to problems in fluid mechanics (76M10) Magnetohydrodynamics and electrohydrodynamics (76W05) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60)

Related Items

New error analysis and recovery technique of a class of fully discrete finite element methods for the dynamical inductionless MHD equations ⋮ Dual-robust iterative analysis of divergence-conforming IPDG FEM for thermally coupled inductionless MHD system ⋮ New error analysis of charge-conservative finite element methods for stationary inductionless MHD equations ⋮ Electric potential-robust iterative analysis of charge-conservative conforming FEM for thermally coupled inductionless MHD system ⋮ A decoupled, unconditionally energy stable and charge-conservative finite element method for inductionless magnetohydrodynamic equations

Cites Work

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• A consistent and conservative scheme for incompressible MHD flows at a low magnetic Reynolds number. III: On a staggered mesh
• Stable finite element methods preserving \(\nabla \cdot \boldsymbol{B}=0\) exactly for MHD models
• Approximation of the inductionless MHD problem using a stabilized finite element method
• Block recursive LU preconditioners for the thermally coupled incompressible inductionless MHD problem
• Magnetohydrodynamics. Transl. from the French by A. F. Wright, typeset by C. Philippe
• Mixed finite element methods for stationary incompressible magneto-hydrodynamics
• On the regularity criteria for weak solutions to the magnetohydrodynamic equations
• Numerical analysis of a second order algorithm for simplified magnetohydrodynamic flows
• Iterative methods in penalty finite element discretization for the steady MHD equations
• A current density conservative scheme for incompressible MHD flows at a low magnetic Reynolds number. I: On a rectangular collocated grid system
• A current density conservative scheme for incompressible MHD flows at a low magnetic Reynolds number. II: On an arbitrary collocated mesh
• Partial regularity of suitable weak solutions to the incompressible magnetohydrodynamic equa\-tions
• Error estimates of finite element methods for nonstationary thermal convection problems with temperature-dependent coefficients
• An Introduction to Magnetohydrodynamics
• Some mathematical questions related to the mhd equations
• Mathematical Methods for the Magnetohydrodynamics of Liquid Metals
• Finite Element Methods for Navier-Stokes Equations
• Finite Element Approximation of the Nonstationary Navier–Stokes Problem. I. Regularity of Solutions and Second-Order Error Estimates for Spatial Discretization
• Mixed and Hybrid Finite Element Methods
• The initial value problem for a generalized Boussinesq model
• A fully divergence-free finite element method for magnetohydrodynamic equations
• A prioriestimates and optimal finite element approximation of the MHD flow in smooth domains
• Finite Element Methods for Maxwell's Equations
• Mixed Finite Element Methods and Applications
• A Charge-Conservative Finite Element Method for Inductionless MHD Equations. Part I: Convergence
• Unconditional convergence of the Euler semi-implicit scheme for the three-dimensional incompressible MHD equations
• A semi‐discrete defect correction finite element method for unsteady incompressible magnetohydrodynamics equations
• Finite Difference Approximation for Pricing the American Lookback Option