Variational discretization of parabolic control problems in the presence of pointwise state constraints
نویسندگان
چکیده
We consider a parabolic optimal control problem with pointwise state constraints. The optimization problem is approximated by a discrete control problem based on a discretization of the state equation by linear finite elements in space and a discontinuous Galerkin scheme in time. Error bounds for control and state are obtained both in two and three space dimensions. These bounds follow from uniform estimates for the discretization error of the state under natural regularity requirements. Mathematics Subject Classification (2000): 49J20, 49K20, 35B37
منابع مشابه
VARIATIONAL DISCRETIZATION AND MIXED METHODS FOR SEMILINEAR PARABOLIC OPTIMAL CONTROL PROBLEMS WITH INTEGRAL CONSTRAINT
The aim of this work is to investigate the variational discretization and mixed finite element methods for optimal control problem governed by semi linear parabolic equations with integral constraint. The state and co-state are approximated by the lowest order Raviart-Thomas mixed finite element spaces and the control is not discreted. Optimal error estimates in L2 are established for the state...
متن کاملA Priori Error Estimates for Space-Time Finite Element Discretization of Parabolic Optimal Control Problems
In this article we summarize recent results on a priori error estimates for space-time finite element discretizations of linear-quadratic parabolic optimal control problems. We consider the following three cases: problems without inequality constraints, problems with pointwise control constraints, and problems with state constraints pointwise in time. For all cases, error estimates with respect...
متن کاملA Priori Error Estimates for Space-Time Finite Element Discretization of Parabolic Optimal Control Problems Part II: Problems with Control Constraints
This paper is the second part of our work on a priori error analysis for finite element discretizations of parabolic optimal control problems. In the first part [18] problems without control constraints were considered. In this paper we derive a priori error estimates for space-time finite element discretizations of parabolic optimal control problems with pointwise inequality constraints on the...
متن کاملA Priori Error Estimates for Finite Element Discretizations of Parabolic Optimization Problems with Pointwise State Constraints in Time
In this paper, we consider an optimal control problem, which is governed by a linear parabolic equation and is subject to state constraints pointwise in time. Optimal order error estimates are developed for a space-time finite element discretization of this problem. Numerical examples confirm the theoretical results. As a byproduct of our analysis, we derive a new regularity result for the opti...
متن کاملHamburger Beiträge zur Angewandten Mathematik A Priori Error Estimates for a Finite Element Discretization of Parabolic Optimization Problems with Pointwise Constraints in Time on Mean Values of the Gradient of the State
This article is concerned with the discretization of parabolic optimization problems subject to pointwise in time constraints on mean values of the derivative of the state variable. Central component of the analysis are a priori error estimates for the dG(0)-cG(1) discretization of the parabolic partial differential equation (PDE) in the L∞(0, T ;H1 0 (Ω))-norm, together with corresponding esti...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2009