A Posteriori Error Estimates of Recovery Type for Distributed Convex Optimal Control Problems

Authors:
Ruo Li;Wenbin Liu;Ningning Yan
Affiliations:
School of Mathematical Sciences, Peking University, Beijing, China 100871;KBS & Institute of Mathematics and Statistics, The University of Kent, Canterbury, England CT2 7NF;Institute of Systems Science, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China
Venue:
Journal of Scientific Computing
Year:
2007

Citing 7
Cited 3

The superconvergent patch recovery (SPR) and adaptive finite element refinement

Computer Methods in Applied Mechanics and Engineering - Special issue on reliability in computational mechanics
Edge Residuals Dominate A Posteriori Error Estimates for Low Order Finite Element Methods

SIAM Journal on Numerical Analysis
Finite Element Method for Elliptic Problems

Finite Element Method for Elliptic Problems
Adaptive Finite Element Methods for Optimal Control of Partial Differential Equations: Basic Concept

SIAM Journal on Control and Optimization
A Posteriori Error Estimates for Convex Boundary Control Problems

SIAM Journal on Numerical Analysis
A Posteriori Error Estimates for Control Problems Governed by Stokes Equations

SIAM Journal on Numerical Analysis
Adaptive Finite Element Approximation for Distributed Elliptic Optimal Control Problems

SIAM Journal on Control and Optimization

Superconvergence for Optimal Control Problems Governed by Semi-linear Elliptic Equations

Journal of Scientific Computing
A Posteriori Error Estimates for Finite Element Approximation of Unsteady Incompressible Stochastic Navier-Stokes Equations

SIAM Journal on Numerical Analysis
A posteriori error analysis for discontinuous finite volume methods of elliptic interface problems

Journal of Computational and Applied Mathematics

Quantified Score

Hi-index	0.00

Visualization

Abstract

In this paper, we derive a posteriori error estimates of recovery type, and present the superconvergence analysis for the finite element approximation of distributed convex optimal control problems. We provide a posteriori error estimates of recovery type for both the control and the state approximation, which are generally equivalent. Under some stronger assumptions, they are further shown to be asymptotically exact. Such estimates, which are apparently not available in the literature, can be used to construct adaptive finite element approximation schemes and as a reliability bound for the control problems. Numerical results demonstrating our theoretical results are also presented in this paper.