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

## Abstract

Not provided.

- Authors:

- Publication Date:

- Research Org.:
- Pennsylvania State Univ., University Park, PA (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC)

- OSTI Identifier:
- 1533266

- DOE Contract Number:
- SC0014400

- Resource Type:
- Journal Article

- Journal Name:
- Numerische Mathematik

- Additional Journal Information:
- Journal Volume: 135; Journal Issue: 2; Journal ID: ISSN 0029-599X

- Publisher:
- Springer Berlin Heidelberg

- Country of Publication:
- United States

- Language:
- English

- Subject:
- Mathematics

### 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.
```

```
@article{osti_1533266,
```

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}

}

Other availability

Save to My Library

You must Sign In or Create an Account in order to save documents to your library.

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

- Armero, F.; Simo, J. C.
- Computer Methods in Applied Mechanics and Engineering, Vol. 131, Issue 1-2

##
Finite element exterior calculus, homological techniques, and applications

journal, May 2006

- Arnold, Douglas N.; Falk, Richard S.; Winther, Ragnar
- Acta Numerica, Vol. 15

##
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

##
On an unconditionally convergent stabilized finite element approximation of resistive magnetohydrodynamics

journal, February 2013

- Badia, Santiago; Codina, Ramon; Planas, Ramon
- Journal of Computational Physics, Vol. 234

##
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

##
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

##
The Effect of Nonzero ∇ · B on the numerical solution of the magnetohydrodynamic equations

journal, May 1980

- Brackbill, J. U.; Barnes, D. C.
- Journal of Computational Physics, Vol. 35, Issue 3

##
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

##
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

##
Eddy Current and Temperature Simulation in thin Moving Metal Strips

journal, January 1996

- Conraths, H. -J.
- International Journal for Numerical Methods in Engineering, Vol. 39, Issue 1

##
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

##
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

##
Hyperbolic Divergence Cleaning for the MHD Equations

journal, January 2002

- Dedner, A.; Kemm, F.; Kröner, D.
- Journal of Computational Physics, Vol. 175, Issue 2

##
Modeling of electromagnetic absorption/scattering problems using hp-adaptive finite elements

journal, January 1998

- Demkowicz, L.; Vardapetyan, L.
- Computer Methods in Applied Mechanics and Engineering, Vol. 152, Issue 1-2

##
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

##
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

##
Simulation of magnetohydrodynamic flows - A constrained transport method

journal, September 1988

- Evans, Charles R.; Hawley, John F.
- The Astrophysical Journal, Vol. 332

##
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

##
On the existence, uniqueness, and finite element approximation of solutions of the equations of stationary, incompressible magnetohydrodynamics

journal, May 1991

- Gunzburger, Max D.; Meir, Amnon J.; Peterson, Janet S.
- Mathematics of Computation, Vol. 56, Issue 194

##
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

##
Finite elements in computational electromagnetism

journal, January 2002

- Hiptmair, R.
- Acta Numerica, Vol. 11

##
Symmetric Coupling for Eddy Current Problems

journal, January 2002

- Hiptmair, R.
- SIAM Journal on Numerical Analysis, Vol. 40, Issue 1

##
Locally Divergence-Free Discontinuous Galerkin Methods for MHD Equations

journal, June 2005

- Li, Fengyan; Shu, Chi-Wang
- Journal of Scientific Computing, Vol. 22-23, Issue 1-3

##
Arbitrary order exactly divergence-free central discontinuous Galerkin methods for ideal MHD equations

journal, March 2012

- Li, Fengyan; Xu, Liwei
- Journal of Computational Physics, Vol. 231, Issue 6

##
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

##
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

##
Energy and helicity preserving schemes for hydro- and magnetohydro-dynamics flows with symmetry

journal, October 2004

- Liu, Jian-Guo; Wang, Wei-Cheng
- Journal of Computational Physics, Vol. 200, Issue 1

##
On the divergence-free condition in Godunov-type schemes for ideal magnetohydrodynamics: the upwind constrained transport method

journal, March 2004

- Londrillo, P.; Del Zanna, L.
- Journal of Computational Physics, Vol. 195, Issue 1

##
Mixed finite elements in ?3

journal, September 1980

- Nedelec, J. C.
- Numerische Mathematik, Vol. 35, Issue 3

##
A new family of mixed finite elements in ?3

journal, January 1986

- N�d�lec, J. C.
- Numerische Mathematik, Vol. 50, Issue 1

##
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

##
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

##
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

##
Mixed finite element methods for stationary incompressible magneto?hydrodynamics

journal, February 2004

- Sch�tzau, Dominik
- Numerische Mathematik, Vol. 96, Issue 4

##
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

##
The ∇·B=0 Constraint in Shock-Capturing Magnetohydrodynamics Codes

journal, July 2000

- Tóth, Gábor
- Journal of Computational Physics, Vol. 161, Issue 2

##
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

##
Finite element approximation for equations of magnetohydrodynamics

journal, August 1999

- Wiedmer, Matthias
- Mathematics of Computation, Vol. 69, Issue 229