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Title: Stable finite element methods preserving $$\nabla \cdot \varvec{B}=0$$ ∇ · B = 0 exactly for MHD models


Not provided.

; ;
Publication Date:
Research Org.:
Pennsylvania State Univ., University Park, PA (United States)
Sponsoring Org.:
USDOE Office of Science (SC)
OSTI Identifier:
DOE Contract Number:  
Resource Type:
Journal Article
Journal Name:
Numerische Mathematik
Additional Journal Information:
Journal Volume: 135; Journal Issue: 2; Journal ID: ISSN 0029-599X
Springer Berlin Heidelberg
Country of Publication:
United States

Citation Formats

Hu, Kaibo, Ma, Yicong, and Xu, Jinchao. Stable finite element methods preserving $$\nabla \cdot \varvec{B}=0$$ ∇ · B = 0 exactly for MHD models. United States: N. p., 2016. Web. doi:10.1007/s00211-016-0803-4.
Hu, Kaibo, Ma, Yicong, & Xu, Jinchao. Stable finite element methods preserving $$\nabla \cdot \varvec{B}=0$$ ∇ · B = 0 exactly for MHD models. United States. doi:10.1007/s00211-016-0803-4.
Hu, Kaibo, Ma, Yicong, and Xu, Jinchao. Mon . "Stable finite element methods preserving $$\nabla \cdot \varvec{B}=0$$ ∇ · B = 0 exactly for MHD models". United States. doi:10.1007/s00211-016-0803-4.
title = {Stable finite element methods preserving $$\nabla \cdot \varvec{B}=0$$ ∇ · B = 0 exactly for MHD models},
author = {Hu, Kaibo and Ma, Yicong and Xu, Jinchao},
abstractNote = {Not provided.},
doi = {10.1007/s00211-016-0803-4},
journal = {Numerische Mathematik},
issn = {0029-599X},
number = 2,
volume = 135,
place = {United States},
year = {2016},
month = {3}

Works referenced in this record:

Long-term dissipativity of time-stepping algorithms for an abstract evolution equation with applications to the incompressible MHD and Navier-Stokes equations
journal, April 1996

Finite element exterior calculus, homological techniques, and applications
journal, May 2006

Finite element exterior calculus: from Hodge theory to numerical stability
journal, January 2010

  • Arnold, Douglas N.; Falk, Richard S.; Winther, Ragnar
  • Bulletin of the American Mathematical Society, Vol. 47, Issue 2
  • DOI: 10.1090/S0273-0979-10-01278-4

On an unconditionally convergent stabilized finite element approximation of resistive magnetohydrodynamics
journal, February 2013

A Comparison between Divergence‐Cleaning and Staggered‐Mesh Formulations for Numerical Magnetohydrodynamics
journal, February 2004

  • Balsara, Dinshaw S.; Kim, Jongsoo
  • The Astrophysical Journal, Vol. 602, Issue 2
  • DOI: 10.1086/381051

A Staggered Mesh Algorithm Using High Order Godunov Fluxes to Ensure Solenoidal Magnetic Fields in Magnetohydrodynamic Simulations
journal, March 1999

  • Balsara, Dinshaw S.; Spicer, Daniel S.
  • Journal of Computational Physics, Vol. 149, Issue 2
  • DOI: 10.1006/jcph.1998.6153

The Effect of Nonzero ∇ · B on the numerical solution of the magnetohydrodynamic equations
journal, May 1980

Divergence-Free $\boldsymbol{\mathcal{H}}(\mathbf{div})$ -Conforming Hierarchical Bases for Magnetohydrodynamics (MHD)
journal, March 2013

  • Cai, Wei; Wu, Jian; Xin, Jianguo
  • Communications in Mathematics and Statistics, Vol. 1, Issue 1
  • DOI: 10.1007/s40304-013-0003-9

Locally divergence-free discontinuous Galerkin methods for the Maxwell equations
journal, March 2004

  • Cockburn, Bernardo; Li, Fengyan; Shu, Chi-Wang
  • Journal of Computational Physics, Vol. 194, Issue 2
  • DOI: 10.1016/

Eddy Current and Temperature Simulation in thin Moving Metal Strips
journal, January 1996

A New Approximate Block Factorization Preconditioner for Two-Dimensional Incompressible (Reduced) Resistive MHD
journal, January 2013

  • Cyr, Eric C.; Shadid, John N.; Tuminaro, Raymond S.
  • SIAM Journal on Scientific Computing, Vol. 35, Issue 3
  • DOI: 10.1137/12088879X

On the Divergence‐free Condition and Conservation Laws in Numerical Simulations for Supersonic Magnetohydrodynamical Flows
journal, February 1998

  • Dai, Wenlong; Woodward, Paul R.
  • The Astrophysical Journal, Vol. 494, Issue 1
  • DOI: 10.1086/305176

Hyperbolic Divergence Cleaning for the MHD Equations
journal, January 2002

  • Dedner, A.; Kemm, F.; Kröner, D.
  • Journal of Computational Physics, Vol. 175, Issue 2
  • DOI: 10.1006/jcph.2001.6961

Modeling of electromagnetic absorption/scattering problems using hp-adaptive finite elements
journal, January 1998

A Simple Preconditioner for a Discontinuous Galerkin Method for the Stokes Problem
journal, August 2013

  • Ayuso de Dios, Blanca; Brezzi, Franco; Marini, L. Donatella
  • Journal of Scientific Computing, Vol. 58, Issue 3
  • DOI: 10.1007/s10915-013-9758-0

Block Preconditioners Based on Approximate Commutators
journal, January 2006

  • Elman, Howard; Howle, Victoria E.; Shadid, John
  • SIAM Journal on Scientific Computing, Vol. 27, Issue 5
  • DOI: 10.1137/040608817

Simulation of magnetohydrodynamic flows - A constrained transport method
journal, September 1988

  • Evans, Charles R.; Hawley, John F.
  • The Astrophysical Journal, Vol. 332
  • DOI: 10.1086/166684

Mixed finite element approximation of an MHD problem involving conducting and insulating regions: The 3D case
journal, June 2003

  • Guermond, J. L.; Minev, P. D.
  • Numerical Methods for Partial Differential Equations, Vol. 19, Issue 6
  • DOI: 10.1002/num.10067

On the existence, uniqueness, and finite element approximation of solutions of the equations of stationary, incompressible magnetohydrodynamics
journal, May 1991

An unstaggered constrained transport method for the 3D ideal magnetohydrodynamic equations
journal, May 2011

  • Helzel, Christiane; Rossmanith, James A.; Taetz, Bertram
  • Journal of Computational Physics, Vol. 230, Issue 10
  • DOI: 10.1016/

Finite elements in computational electromagnetism
journal, January 2002

Symmetric Coupling for Eddy Current Problems
journal, January 2002

Locally Divergence-Free Discontinuous Galerkin Methods for MHD Equations
journal, June 2005

Arbitrary order exactly divergence-free central discontinuous Galerkin methods for ideal MHD equations
journal, March 2012

Performance of fully coupled algebraic multilevel domain decomposition preconditioners for incompressible flow and transport
journal, January 2006

  • Lin, Paul T.; Sala, Marzio; Shadid, John N.
  • International Journal for Numerical Methods in Engineering, Vol. 67, Issue 2
  • DOI: 10.1002/nme.1624

An Energy-Preserving MAC–Yee Scheme for the Incompressible MHD Equation
journal, November 2001

  • Liu, Jian-Guo; Wang, Wei-Cheng
  • Journal of Computational Physics, Vol. 174, Issue 1
  • DOI: 10.1006/jcph.2001.6772

Energy and helicity preserving schemes for hydro- and magnetohydro-dynamics flows with symmetry
journal, October 2004

On the divergence-free condition in Godunov-type schemes for ideal magnetohydrodynamics: the upwind constrained transport method
journal, March 2004

Mixed finite elements in ?3
journal, September 1980

A new family of mixed finite elements in ?3
journal, January 1986

A Block Preconditioner for an Exact Penalty Formulation for Stationary MHD
journal, January 2014

  • Phillips, Edward G.; Elman, Howard C.; Cyr, Eric C.
  • SIAM Journal on Scientific Computing, Vol. 36, Issue 6
  • DOI: 10.1137/140955082

Convergent finite element discretizations of the nonstationary incompressible magnetohydrodynamics system
journal, August 2008

  • Prohl, Andreas
  • ESAIM: Mathematical Modelling and Numerical Analysis, Vol. 42, Issue 6
  • DOI: 10.1051/m2an:2008034

An Unstaggered, High‐Resolution Constrained Transport Method for Magnetohydrodynamic Flows
journal, January 2006

  • Rossmanith, James A.
  • SIAM Journal on Scientific Computing, Vol. 28, Issue 5
  • DOI: 10.1137/050627022

Mixed finite element methods for stationary incompressible magneto?hydrodynamics
journal, February 2004

Towards a scalable fully-implicit fully-coupled resistive MHD formulation with stabilized FE methods
journal, October 2010

  • Shadid, J. N.; Pawlowski, R. P.; Banks, J. W.
  • Journal of Computational Physics, Vol. 229, Issue 20
  • DOI: 10.1016/

The ∇·B=0 Constraint in Shock-Capturing Magnetohydrodynamics Codes
journal, July 2000

On a multilevel preconditioning module for unstructured mesh Krylov solvers: two-level Schwarz
journal, March 2002

  • Tuminaro, R. S.; Tong, C. H.; Shadid, J. N.
  • Communications in Numerical Methods in Engineering, Vol. 18, Issue 6
  • DOI: 10.1002/cnm.478

Finite element approximation for equations of magnetohydrodynamics
journal, August 1999