L∞-asymptotic behavior for a finite element approximation in parabolic quasi-variational inequalities related to impulse control problem

2011 ◽  
Vol 217 (14) ◽  
pp. 6443-6450 ◽  
Author(s):  
Salah Boulaaras ◽  
Mohamed Haiour
Keyword(s):  
Finite Element ◽  
Asymptotic Behavior ◽  
Variational Inequalities ◽  
Control Problem ◽  
Impulse Control ◽  
Finite Element Approximation ◽  
Element Approximation ◽  
Impulse Control Problem

scholarly journals A New Approach to Asymptotic Behavior for a Finite Element Approximation in Parabolic Variational Inequalities

2011 ◽  
Vol 2011 ◽  
pp. 1-15 ◽  
Author(s):  
Salah Boulaaras ◽  
Mohamed Haiour
Keyword(s):  
Finite Element ◽  
Asymptotic Behavior ◽  
Variational Inequalities ◽  
Finite Element Approximation ◽  
Uniform Norm ◽  
Element Approximation ◽  
New Approach ◽  
Elliptic Variational Inequalities ◽  
Energy Behavior ◽  
Spatial Approximation

The paper deals with the theta time scheme combined with a finite element spatial approximation of parabolic variational inequalities. The parabolic variational inequalities are transformed into noncoercive elliptic variational inequalities. A simple result to time energy behavior is proved, and a new iterative discrete algorithm is proposed to show the existence and uniqueness. Moreover, its convergence is established. Furthermore, a simple proof to asymptotic behavior in uniform norm is given.

scholarly journals Adaptive Semidiscrete Finite Element Methods for Semilinear Parabolic Integrodifferential Optimal Control Problem with Control Constraint

2013 ◽  
Vol 2013 ◽  
pp. 1-11
Author(s):  
Zuliang Lu
Keyword(s):  
Optimal Control ◽  
Finite Element ◽  
Optimal Control Problem ◽  
Control Problem ◽  
A Posteriori Error Estimates ◽  
Finite Element Approximation ◽  
Element Approximation ◽  
Adaptive Finite Element ◽  
Element Discretization ◽  
Semilinear Parabolic

The aim of this work is to study the semidiscrete finite element discretization for a class of semilinear parabolic integrodifferential optimal control problems. We derive a posteriori error estimates inL2(J;L2(Ω))-norm andL2(J;H1(Ω))-norm for both the control and coupled state approximations. Such estimates can be used to construct reliable adaptive finite element approximation for semilinear parabolic integrodifferential optimal control problem. Furthermore, we introduce an adaptive algorithm to guide the mesh refinement. Finally, a numerical example is given to demonstrate the theoretical results.

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