Proceedings ArticleDOI
Error estimates of variational discretization and fully discrete mixed finite element methods for semilinear parabolic optimal control problem
Zuliang Lu,Xiao Huang +1 more
- Vol. 1, pp 142-145
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TLDR
This paper studies the variational discretization and fully discrete mixed finite element methods for optimal control problem governed by semilinear parabolic equations and derives a priori error estimates both for the coupled state and the control approximation.Abstract:
In this paper we study the variational discretization and fully discrete mixed finite element methods for optimal control problem governed by semilinear parabolic equations. The space discretization of the state variable is done using usual mixed finite elements, whereas the time discretization is based on difference methods. The state and the co-state are approximated by the lowest order Raviart-Thomas mixed finite element spaces and the control is not discreted. Then we derive a priori error estimates both for the coupled state and the control approximation. Finally, we present a numerical example which confirms our theoretical results.read more
References
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Book ChapterDOI
A mixed finite element method for 2-nd order elliptic problems
P. A. Raviart,J. M. Thomas +1 more
Book
Galerkin Finite Element Methods for Parabolic Problems
TL;DR: The standard Galerkin method is based on more general approximations of the elliptic problem as discussed by the authors, and is used to solve problems in algebraic systems at the time level.
Journal ArticleDOI
A variational discretization concept in control constrained optimization: the linear-quadratic case
TL;DR: It is shown that the new discretization concept for optimal control problems with control constraints is numerically implementable with only slight increase in program management and an optimal error estimate is proved.
Journal ArticleDOI
Error Estimates for the Numerical Approximation of a Semilinear Elliptic Control Problem
TL;DR: The uniform convergence of discretized controls to optimal controls is proven under natural assumptions and error estimates for optimal controls in the maximum norm are estimated.
Journal ArticleDOI
Approximation of a class of optimal control problems with order of convergence estimates
TL;DR: In this paper, an approximation scheme for a class of optimal control problems is presented, and an order of convergence estimate is developed for the error in the approximation of both the optimal control and the solution of the control equation.
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