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Numerical Approximations of the Relative Rearrangement: The piecewise linear case. Application to some Nonlocal Problems

Published online by Cambridge University Press:  15 April 2002

Jean-Michel Rakotoson  and
Maria Luisa Seoane
Jean-Michel Rakotoson
Affiliation:
Département de Mathématiques, Université de Poitiers, boulevard 3, Téléport 2, B.P. 179, 86960 Futuroscope, France.
Maria Luisa Seoane
Affiliation:
Departamento de Matemática Aplicada, Facultad de Matemáticas, Campus Universitario, 15706 Santiago de Compostela, Spain.
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Abstract

We first prove an abstract result for a class of nonlocal problems using fixed point method. We apply this result to equations revelant from plasma physic problems. These equations contain terms like monotone or relative rearrangement of functions. So, we start the approximation study by using finite element to discretize this nonstandard quantities. We end the paper by giving a numerical resolution of a model containing those terms.

Keywords

Monotone decreasing and relative rearrangementsnonlocal problemsnumerical approximations.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 34 , Issue 2: Special issue for R. Teman's 60th birthday , March 2000 , pp. 477 - 499
Copyright
© EDP Sciences, SMAI, 2000

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