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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
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 nonlocalproblems using fixed point method. We apply this result toequations revelant from plasma physic problems. These equationscontain terms like monotone or relative rearrangement of functions.So, we start the approximation study by using finite element todiscretize this nonstandard quantities. We end the paper by giving a numerical resolution of a model containing those terms.

Type
Research Article
Copyright
© EDP Sciences, SMAI, 2000

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