A Linear Stabilized Incompressible Magnetohydrodynamic Problem with Magnetic Pressure

Shahid Hussain, Ahmed Bakhet (), Ghada AlNemer and Mohammed Zakarya
Additional contact information
Shahid Hussain: College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, China
Ahmed Bakhet: College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, China
Ghada AlNemer: Department of Mathematical Science, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 105862, Riyadh 11656, Saudi Arabia
Mohammed Zakarya: Department of Mathematics, College of Science, King Khalid University, P.O. Box 9004, Abha 61413, Saudi Arabia

Mathematics, 2024, vol. 12, issue 12, 1-19

Abstract: The objective of this article is to examine, stabilize, and linearize the incompressible magnetohydrodynamic model equations. The approximate solutions are carried out through the lowest equal order mixed finite element (FE) approach, involving variables such as fluid velocity, hydro pressure, magnetic field, and magnetic pressure. The formulation of the variational form for the approximate solution necessitates the use of a pair of approximating spaces. However, these spaces cannot be arbitrarily chosen; they must adhere to strict stability conditions, notably the Ladyzhenskaya–Babuska–Brezzi (LBB) or inf-sup condition. This study addresses the absence of stabilization and linearization techniques in the incompressible magnetohydrodynamic model equations using the lowest equal order mixed finite element approach. The article introduces a stabilization technique to meet two stability conditions, proving its existence and uniqueness. This novel approach was not previously explored in the literature. The proposed stabilized technique does not necessitate parameters or computing higher-order derivatives, making it computationally efficient. The study offers numerical tests demonstrating optimal convergence and effectiveness of the revised approach in two-dimensional settings.

Keywords: lowest equal order FE; magnetohydrodynamic equations; two inf-sup conditions; stabilized method (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/12/12/1839/pdf (application/pdf)
https://www.mdpi.com/2227-7390/12/12/1839/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:12:y:2024:i:12:p:1839-:d:1414259

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().