Nodal-based finite element methods with local projection stabilization for linearized incompressible magnetohydrodynamics

Benjamin Wacker; Daniel Arndt; Gert Lube

doi:10.1016/j.cma.2016.01.004

Nodal-based finite element methods with local projection stabilization for linearized incompressible magnetohydrodynamics

Benjamin Wacker
, Daniel Arndt
, Gert Lube

Research output: Contribution to journal › Article › peer-review

19 Scopus citations

Abstract

We consider the linearized resistive magnetohydrodynamics (MHD) model in incompressible media and its numerical solution. Conforming nodal-based finite element approximations of the MHD model both for inf-sup stable and equal order finite elements with respect to velocity and pressure are considered. As opposed to a residual-based stabilization method by Badia et al. (2013), we consider a local projection stabilization for the numerical solution. A detailed stability and error analysis for the arising discrete problem is given. Some numerical experiments like Hartmann's MHD problem and singular solutions are examined.

Original language	English
Pages (from-to)	170-192
Number of pages	23
Journal	Computer Methods in Applied Mechanics and Engineering
Volume	302
DOIs	https://doi.org/10.1016/j.cma.2016.01.004
State	Published - Apr 15 2016
Externally published	Yes

Funding

The research of D. Arndt was supported by CRC 963 via German Research Foundation (DFG) . The research of B. Wacker was supported by RTG 1023 via German Research Foundation (DFG) .

Keywords

Inf-sup stable and equal-order interpolation
Local projection stabilization
Nodal-based finite element methods
Resistive incompressible magnetohydrodynamics

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10.1016/j.cma.2016.01.004

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title = "Nodal-based finite element methods with local projection stabilization for linearized incompressible magnetohydrodynamics",

abstract = "We consider the linearized resistive magnetohydrodynamics (MHD) model in incompressible media and its numerical solution. Conforming nodal-based finite element approximations of the MHD model both for inf-sup stable and equal order finite elements with respect to velocity and pressure are considered. As opposed to a residual-based stabilization method by Badia et al. (2013), we consider a local projection stabilization for the numerical solution. A detailed stability and error analysis for the arising discrete problem is given. Some numerical experiments like Hartmann's MHD problem and singular solutions are examined.",

keywords = "Inf-sup stable and equal-order interpolation, Local projection stabilization, Nodal-based finite element methods, Resistive incompressible magnetohydrodynamics",

author = "Benjamin Wacker and Daniel Arndt and Gert Lube",

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T1 - Nodal-based finite element methods with local projection stabilization for linearized incompressible magnetohydrodynamics

AU - Wacker, Benjamin

AU - Arndt, Daniel

AU - Lube, Gert

PY - 2016/4/15

Y1 - 2016/4/15

N2 - We consider the linearized resistive magnetohydrodynamics (MHD) model in incompressible media and its numerical solution. Conforming nodal-based finite element approximations of the MHD model both for inf-sup stable and equal order finite elements with respect to velocity and pressure are considered. As opposed to a residual-based stabilization method by Badia et al. (2013), we consider a local projection stabilization for the numerical solution. A detailed stability and error analysis for the arising discrete problem is given. Some numerical experiments like Hartmann's MHD problem and singular solutions are examined.

AB - We consider the linearized resistive magnetohydrodynamics (MHD) model in incompressible media and its numerical solution. Conforming nodal-based finite element approximations of the MHD model both for inf-sup stable and equal order finite elements with respect to velocity and pressure are considered. As opposed to a residual-based stabilization method by Badia et al. (2013), we consider a local projection stabilization for the numerical solution. A detailed stability and error analysis for the arising discrete problem is given. Some numerical experiments like Hartmann's MHD problem and singular solutions are examined.

KW - Inf-sup stable and equal-order interpolation

KW - Local projection stabilization

KW - Nodal-based finite element methods

KW - Resistive incompressible magnetohydrodynamics

UR - https://www.scopus.com/pages/publications/84956612831

U2 - 10.1016/j.cma.2016.01.004

DO - 10.1016/j.cma.2016.01.004

M3 - Article

AN - SCOPUS:84956612831

SN - 0045-7825

VL - 302

SP - 170

EP - 192

JO - Computer Methods in Applied Mechanics and Engineering

JF - Computer Methods in Applied Mechanics and Engineering

ER -

Nodal-based finite element methods with local projection stabilization for linearized incompressible magnetohydrodynamics

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Keywords

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