Analysis for the space-time a posteriori error estimates for mixed finite element solutions of parabolic optimal control problems

This paper investigates the space-time residual-based a posteriori error bounds of the mixed finite element method for the optimal control problem governed by the parabolic equation in a bounded convex domain. For the spatial discretization of the state and co-state variables, the lowest-order Ravia...

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Bibliographic Details
Published in:Numerical algorithms Vol. 96; no. 2; pp. 879 - 924
Main Authors: Shakya, Pratibha, Kumar Sinha, Rajen
Format: Journal Article
Language:English
Published: New York Springer US 01.06.2024
Springer Nature B.V
Subjects:
Algebra
Algorithms
Approximation
Computer Science
Discretization
Error analysis
Estimates
Estimators
Finite element method
Implicit methods
Numeric Computing
Numerical Analysis
Optimal control
Original Paper
Spacetime
Theory of Computation
Variables
The backward-Euler method
65N15
Mixed finite element method
Variational discretization
49J20
A posteriori error estimates
Parabolic optimal control problems
65N30
ISSN:1017-1398, 1572-9265
Online Access:Get full text
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Summary:This paper investigates the space-time residual-based a posteriori error bounds of the mixed finite element method for the optimal control problem governed by the parabolic equation in a bounded convex domain. For the spatial discretization of the state and co-state variables, the lowest-order Raviart-Thomas spaces are utilized, although for the control variable, variational discretization technique is used. The backward-Euler implicit method is applied for temporal discretization. To provide a posteriori error estimates for the state and control variables in the L ∞ ( L 2 ) -norm, an elliptic reconstruction approach paired with an energy strategy is utilized. The reliability and efficiency of the a posteriori error estimators are discussed. The effectiveness of the estimators is finally confirmed through the numerical tests.
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ISSN:1017-1398
1572-9265
DOI:10.1007/s11075-023-01669-9