Volume 23, Issue 3
Least-Squares Mixed Finite Element Methods for the Incompressible Magnetohydrodynamic Equations

Shao-Qin Gao

DOI:

J. Comp. Math., 23 (2005), pp. 327-336

Published online: 2005-06

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  • Abstract

Least-squares mixed finite element methods are proposed and analyzed for the incompressible magnetohydrodynamic equations, where the two vorticities are additionally introduced as independent variables in order that the primal equations are transformed into the first-order systems. We show that there hold the coerciveness and the optimal error bound in appropriate norms for all variables under consideration, which can be approximated by all kinds of continuous element. Consequently, the Babu$\check{s}$ka-Brezzi condition (i.e. the inf-sup condition) and the indefiniteness are avoided which are essential features of the classical mixed methods.

  • Keywords

The incompressible magnetohydrodynamic equation Vorticity Least-squares mixed finite element method

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@Article{JCM-23-327, author = {}, title = {Least-Squares Mixed Finite Element Methods for the Incompressible Magnetohydrodynamic Equations}, journal = {Journal of Computational Mathematics}, year = {2005}, volume = {23}, number = {3}, pages = {327--336}, abstract = { Least-squares mixed finite element methods are proposed and analyzed for the incompressible magnetohydrodynamic equations, where the two vorticities are additionally introduced as independent variables in order that the primal equations are transformed into the first-order systems. We show that there hold the coerciveness and the optimal error bound in appropriate norms for all variables under consideration, which can be approximated by all kinds of continuous element. Consequently, the Babu$\check{s}$ka-Brezzi condition (i.e. the inf-sup condition) and the indefiniteness are avoided which are essential features of the classical mixed methods. }, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8819.html} }
TY - JOUR T1 - Least-Squares Mixed Finite Element Methods for the Incompressible Magnetohydrodynamic Equations JO - Journal of Computational Mathematics VL - 3 SP - 327 EP - 336 PY - 2005 DA - 2005/06 SN - 23 DO - http://dor.org/ UR - https://global-sci.org/intro/jcm/8819.html KW - The incompressible magnetohydrodynamic equation KW - Vorticity KW - Least-squares mixed finite element method AB - Least-squares mixed finite element methods are proposed and analyzed for the incompressible magnetohydrodynamic equations, where the two vorticities are additionally introduced as independent variables in order that the primal equations are transformed into the first-order systems. We show that there hold the coerciveness and the optimal error bound in appropriate norms for all variables under consideration, which can be approximated by all kinds of continuous element. Consequently, the Babu$\check{s}$ka-Brezzi condition (i.e. the inf-sup condition) and the indefiniteness are avoided which are essential features of the classical mixed methods.
Shao-Qin Gao. (1970). Least-Squares Mixed Finite Element Methods for the Incompressible Magnetohydrodynamic Equations. Journal of Computational Mathematics. 23 (3). 327-336. doi:
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