Numerical approximations of the relative rearrangement : the piecewise linear case. Application to some nonlocal problems
نویسندگان
چکیده
We first prove an abstract resuit for a class of nonlocal problems using fixed point method. We apply this result to équations révélant from plasma physic problems. These équations contain terms like monotone or relative rearrangement of fonctions. 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. Received: May 27, 1999. Revised: October 26 1999.
منابع مشابه
Accurate Piecewise Linear Continuous Approximations to One-Dimensional Curves: Error Estimates and Algorithms
Local and global asymptotic L2 error estimates are derived for piecewise linear continuous approximations to smooth one-dimensional curves in R (n ≥ 1). Based on the estimates and an equidistribution strategy, an algorithm to construct a highly accurate piecewise linear approximation to a one-dimensional curve is devised with a special feature of achieving a desired L2 error. By its generality,...
متن کاملError Estimates for the Numerical Approximation of Boundary Semilinear Elliptic Control Problems. Continuous Piecewise Linear Approximations
We discuss error estimates for the numerical analysis of Neumann boundary control problems. We present some known results about piecewise constant approximations of the control and introduce some new results about continuous piecewise linear approximations. We obtain the rates of convergence in i ^ ( r ) . Error estimates in the uniform norm are also obtained. We also discuss the semidiscretiza...
متن کاملClose interval approximation of piecewise quadratic fuzzy numbers for fuzzy fractional program
The fuzzy approach has undergone a profound structural transformation in the past few decades. Numerous studies have been undertaken to explain fuzzy approach for linear and nonlinear programs. While, the findings in earlier studies have been conflicting, recent studies of competitive situations indicate that fractional programming problem has a positive impact on comparative scenario. We pro...
متن کاملApproximate Pareto Optimal Solutions of Multi objective Optimal Control Problems by Evolutionary Algorithms
In this paper an approach based on evolutionary algorithms to find Pareto optimal pair of state and control for multi-objective optimal control problems (MOOCP)'s is introduced. In this approach, first a discretized form of the time-control space is considered and then, a piecewise linear control and a piecewise linear trajectory are obtained from the discretized time-control space using ...
متن کاملMonotone convergence of finite element approximations of obstacle problems
The purpose of the work is to study the monotone convergence of numerical solutions of obstacle problems under mesh 4 refinement when the obstacle is convex. We prove monotone convergence of piecewise linear finite element approximations for 5 one-dimensional obstacle problems. We demonstrate by giving a example that such monotone convergence will not hold in the 6 two-dimensional case. 7 c © 2...
متن کامل