Volume 34, Number 2, March/April 2000Special issue for R. Teman's 60th birthday
|Page(s)||477 - 499|
|Published online||15 April 2002|
Numerical Approximations of the Relative Rearrangement: The piecewise linear case. Application to some Nonlocal Problems
Département de Mathématiques, Université de Poitiers,
boulevard 3, Téléport 2, B.P. 179, 86960 Futuroscope,
2 Departamento de Matemática Aplicada, Facultad de Matemáticas, Campus Universitario, 15706 Santiago de Compostela, Spain.
Revised: 26 October 1999
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.
Mathematics Subject Classification: 76X05 / 35R30 / 35R35 / 28A75 / 46E30 / 65L60 / 65M60 / 65N30
Key words: Monotone decreasing and relative rearrangements / nonlocal problems / numerical approximations.
© EDP Sciences, SMAI, 2000
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