Mixed Finite Element Method for Dirichlet Boundary Control Problem Governed by Elliptic PDEs

In this paper we study the finite element approximation of Dirichlet boundary control problems governed by elliptic PDEs. Based on a mixed variational scheme, we establish a mixed finite element approximation to the underlying optimal control problem. We consider the optimal control problems posed o...

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Bibliographic Details
Published in:SIAM journal on control and optimization Vol. 49; no. 3; pp. 984 - 1014
Main Authors: Gong, Wei, Yan, Ningning
Format: Journal Article
Language:English
Published: Philadelphia, PA Society for Industrial and Applied Mathematics 01.01.2011
Subjects:
Approximation
Boundary control
Calculus of variations and optimal control
Computational techniques
Dirichlet problem
Estimates
Exact sciences and technology
Finite element analysis
Finite element method
Finite-element and galerkin methods
Mathematical analysis
Mathematical methods in physics
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Optimal control
Optimization
Partial differential equations
Partial differential equations, boundary value problems
Physics
Sciences and techniques of general use
Studies
optimal control problem
Error estimation
Mixed method
19J20
Partial differential equation
Finite element method
Dirichlet boundary control
Elliptic equation
Boundary value problem
mixed finite element
A priori estimation
Dirichlet problem
Galerkin method
a priori error estimate
Optimal control (mathematics)
65N30
ISSN:0363-0129, 1095-7138
Online Access:Get full text
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Summary:In this paper we study the finite element approximation of Dirichlet boundary control problems governed by elliptic PDEs. Based on a mixed variational scheme, we establish a mixed finite element approximation to the underlying optimal control problem. We consider the optimal control problems posed on both polygonal and general smooth domains, and we derive a priori error estimates for optimal control, state, and adjoint state. The optimal and quasi-optimal error estimates are obtained for problems on polygonal and smooth domains, respectively. Numerical experiments are provided to confirm our theoretical results.
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ISSN:0363-0129
1095-7138
DOI:10.1137/100795632