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

Jean-Michel Rakotoson; Maria Luisa Seoane

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

  • Volume: 34, Issue: 2, page 477-499
  • ISSN: 0764-583X

Abstract

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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.

How to cite

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Rakotoson, Jean-Michel, and Seoane, Maria Luisa. "Numerical Approximations of the Relative Rearrangement: The piecewise linear case. Application to some Nonlocal Problems." ESAIM: Mathematical Modelling and Numerical Analysis 34.2 (2010): 477-499. <http://eudml.org/doc/197436>.

@article{Rakotoson2010,
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. },
author = {Rakotoson, Jean-Michel, Seoane, Maria Luisa},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Monotone decreasing and relative rearrangements; nonlocal problems; numerical approximations.; finite element approximation; nonlocal problems; fixed point method; plasma physics; relative rearrangement of functions},
language = {eng},
month = {3},
number = {2},
pages = {477-499},
publisher = {EDP Sciences},
title = {Numerical Approximations of the Relative Rearrangement: The piecewise linear case. Application to some Nonlocal Problems},
url = {http://eudml.org/doc/197436},
volume = {34},
year = {2010},
}

TY - JOUR
AU - Rakotoson, Jean-Michel
AU - Seoane, Maria Luisa
TI - Numerical Approximations of the Relative Rearrangement: The piecewise linear case. Application to some Nonlocal Problems
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2010/3//
PB - EDP Sciences
VL - 34
IS - 2
SP - 477
EP - 499
AB - 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.
LA - eng
KW - Monotone decreasing and relative rearrangements; nonlocal problems; numerical approximations.; finite element approximation; nonlocal problems; fixed point method; plasma physics; relative rearrangement of functions
UR - http://eudml.org/doc/197436
ER -

References

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