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

Authors: Max D. Gunzburger, Amnon J. Meir and Janet S. Peterson
Journal: Math. Comp. 56 (1991), 523-563
MSC: Primary 76W05; Secondary 35Q99, 65N30, 76M10
MathSciNet review: 1066834
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Abstract: We consider the equations of stationary, incompressible magnetohydrodynamics posed in a bounded domain in three dimensions and treat the full, coupled system of equations with inhomogeneous boundary conditions. Under certain conditions on the data, we show that the existence and uniqueness of the solution of a weak formulation of the equations can be guaranteed. We discuss a finite element discretization of the equations and prove an optimal estimate for the error of the approximate solution.

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Article copyright: © Copyright 1991 American Mathematical Society