A Charge-Conservative Finite Element Method for Inductionless MHD Equations. Part II: A Robust Solver

DOI10.1137/19M1260372zbMath1447.65085OpenAlexW2968538350WikidataQ127367313 ScholiaQ127367313MaRDI QIDQ5230640

Ming-Jiu Ni, Weiying Zheng, Ling-Xiao Li

Publication date: 28 August 2019

Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/19m1260372

zbMATH Keywords

block preconditioneraugmented Lagrangian finite element methodfield-of-values-equivalenceconservation of chargesinductionless MHD equations

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Iterative numerical methods for linear systems (65F10) Magnetohydrodynamics and electrohydrodynamics (76W05) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Preconditioners for iterative methods (65F08)

Related Items (10)

New error analysis and recovery technique of a class of fully discrete finite element methods for the dynamical inductionless MHD equations ⋮ Stability and error analysis of the SAV schemes for the inductionless MHD equations ⋮ New error analysis of charge-conservative finite element methods for stationary inductionless MHD equations ⋮ Three interior penalty DG methods for stationary incompressible magnetohydrodynamics ⋮ Local and parallel finite element algorithms based on charge-conservation approximation for the stationary inductionless magnetohydrodynamic problem ⋮ A fully discrete finite element method for a constrained transport model of the incompressible MHD equations ⋮ Electric potential-robust iterative analysis of charge-conservative conforming FEM for thermally coupled inductionless MHD system ⋮ A Scalable Approximate Inverse Block Preconditioner for an Incompressible Magnetohydrodynamics Model Problem ⋮ Error analysis of a conservative finite element scheme for time-dependent inductionless MHD problem ⋮ A decoupled, unconditionally energy stable and charge-conservative finite element method for inductionless magnetohydrodynamic equations

Uses Software

• BoomerAMG

Cites Work

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• On the parameter choice in grad-div stabilization for the Stokes equations
• Grad-div stabilization and subgrid pressure models for the incompressible Navier-Stokes equations
• A mixed finite element method with exactly divergence-free velocities for incompressible magnetohydrodynamics
• 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
• \textit{BoomerAMG}: A parallel algebraic multigrid solver and preconditioner
• Mixed finite element methods for stationary incompressible magneto-hydrodynamics
• A robust solver for the finite element approximation of stationary incompressible MHD equations in 3D
• A low-order Galerkin finite element method for the Navier-Stokes equations of steady incompressible flow: a stabilization issue and iterative methods.
• Robust preconditioners for incompressible MHD models
• Additive Schwarz-based fully coupled implicit methods for resistive Hall magnetohydrodynamic problems
• Grad-div stabilization for the evolutionary Oseen problem with inf-sup stable finite elements
• Operator preconditioning
• 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
• Towards a scalable fully-implicit fully-coupled resistive MHD formulation with stabilized FE methods
• Block Preconditioners for Stable Mixed Nodal and Edge finite element Representations of Incompressible Resistive MHD
• A New Approximate Block Factorization Preconditioner for Two-Dimensional Incompressible (Reduced) Resistive MHD
• Preconditioning discretizations of systems of partial differential equations
• Mathematical Methods for the Magnetohydrodynamics of Liquid Metals
• Numerical solution of saddle point problems
• Finite Element Methods for Navier-Stokes Equations
• Three-Dimensional Finite Element Methods for the Stokes Problem
• A fully divergence-free finite element method for magnetohydrodynamic equations
• Preconditioners for Mixed Finite Element Discretizations of Incompressible MHD Equations
• Analysis of Preconditioners for Saddle-Point Problems
• Local projection stabilization for the Oseen problem
• Grad-div stablilization for Stokes equations
• Mixed Finite Element Methods and Applications
• A Block Preconditioner for an Exact Penalty Formulation for Stationary MHD
• Efficient augmented Lagrangian‐type preconditioning for the Oseen problem using Grad‐Div stabilization
• A Charge-Conservative Finite Element Method for Inductionless MHD Equations. Part I: Convergence
• Nodal Auxiliary Space Preconditioning in H(curl) and H(div) Spaces
• An Augmented Lagrangian‐Based Approach to the Oseen Problem
• Block Preconditioners Based on Approximate Commutators

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