New Analysis of Mixed Finite Element Methods for Incompressible Magnetohydrodynamics
Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review
Author(s)
Related Research Unit(s)
Detail(s)
Original language | English |
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Article number | 72 |
Journal / Publication | Journal of Scientific Computing |
Volume | 95 |
Issue number | 3 |
Online published | 18 Apr 2023 |
Publication status | Published - Jun 2023 |
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Abstract
This paper focuses on new error analysis of a class of mixed FEMs for stationary incompressible magnetohydrodynamics with the standard inf-sup stable velocity-pressure space in cooperation with Navier-Stokes equations and the Nédélec’s edge element for the magnetic field. The methods have been widely used in various numerical simulations in the last several decades, while the existing analysis is not optimal due to the strong coupling of system and the pollution of the lower-order Nédélec’s edge approximation in analysis. In terms of a newly modified Maxwell projection we establish new and optimal error estimates. In particular, we prove that the method based on the commonly-used Taylor-Hood/lowest-order Nédélec’s edge element is efficient and the method provides the second-order accuracy for numerical velocity. Two numerical examples for the problem in both convex and nonconvex polygonal domains are presented, which confirm our theoretical analysis. © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2023
Research Area(s)
- Magnetohydrodynamics, Mixed method
Citation Format(s)
New Analysis of Mixed Finite Element Methods for Incompressible Magnetohydrodynamics. / Huang, Yuchen; Qiu, Weifeng; Sun, Weiwei.
In: Journal of Scientific Computing, Vol. 95, No. 3, 72, 06.2023.
In: Journal of Scientific Computing, Vol. 95, No. 3, 72, 06.2023.
Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review