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Magnetic equations with FreeFem++: The Grad-Shafranov equation & the current hole

Erwan Deriaz, Bruno Despres, Gloria Faccanoni, Kirill Pichon Gostaf, Lise-Marie Imbert-Gérard, Georges Sadaka, Remy Sart (2011)

ESAIM: Proceedings

FreeFem++ [11] is a software for the numerical solution of partial differential equations. It is based on finite element method. The FreeFem++ platform aims at facilitating teaching and basic research through prototyping. For the moment this platform is restricted to the numerical simulations of problems which admit a variational formulation. Our goal in this work is to evaluate the FreeFem++ tool on basic magnetic equations arising in Fusion Plasma...

Magneto-micropolar fluid motion: existence of weak solutions.

Marko A. Rojas-Medar, José Luiz Boldrini (1998)

Revista Matemática Complutense

By using the Galerkin method, we prove the existence of weak solutions for the equations of the magneto-micropolar fluid motion in two and three dimensions in space. In the two-dimensional case, we also prove that such weak solution is unique. We also prove the reproductive property.

Modeling, mathematical and numerical analysis of electrorheological fluids

Michael Růžička (2004)

Applications of Mathematics

Many electrorheological fluids are suspensions consisting of solid particles and a carrier oil. If such a suspension is exposed to a strong electric field the effective viscosity increases dramatically. In this paper we first derive a model which captures this behaviour. For the resulting system of equations we then prove local in time existence of strong solutions for large data. For these solutions we finally derive error estimates for a fully implicit time-discretization.

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