A posteriori error analysis for finite element approximations of parabolic optimal control problems with measure data

DOI10.1016/j.apnum.2018.09.015zbMath1462.65155OpenAlexW2895382797WikidataQ129184035 ScholiaQ129184035MaRDI QIDQ1633315

Pratibha Shakya, Rajen Kumar Sinha

Publication date: 19 December 2018

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.apnum.2018.09.015

zbMATH Keywords

a posteriori error estimatesfinite element approximationsbackward Euler schemeparabolic optimal control problemmeasure data in spacemeasure data in time

Mathematics Subject Classification ID

Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Discrete approximations in optimal control (49M25)

Related Items

Error analysis for finite element approximation of parabolic Neumann boundary control problems ⋮ Error analysis for the finite element approximations of Dirichlet parabolic boundary control problem with measure data ⋮ A posteriori error estimates for parabolic optimal control problems with controls acting on lower dimensional manifolds

Uses Software

• FreeFem++

Cites Work

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• Discrete maximal parabolic regularity for Galerkin finite element methods
• Nonlinear elliptic and parabolic equations involving measure data
• A unified approach to a posteriori error estimation using element residual methods
• A posteriori error estimates for optimal control problems governed by parabolic equations
• \(L^ 2\) estimates for the finite element method for the Dirichlet problem with singular data
• Adaptive finite element method for parabolic equations with Dirac measure
• Adaptive finite element methods for an optimal control problem involving Dirac measures
• Ritz–Galerkin Approximation of the Time Optimal Boundary Control Problem for Parabolic Systems with Dirichlet Boundary Conditions
• Adaptive Finite Element Methods for Parabolic Problems I: A Linear Model Problem
• An optimal control approach to a posteriori error estimation in finite element methods
• A Priori Error Estimates for Space-Time Finite Element Discretization of Parabolic Optimal Control Problems Part II: Problems with Control Constraints
• Some A Posteriori Error Estimators for Elliptic Partial Differential Equations
• On the Smoothing Property of the Galerkin Method for Parabolic Equations
• Pontryagin's Principle for State-Constrained Boundary Control Problems of Semilinear Parabolic Equations
• Theoretical and Numerical Analysis of an Optimal Control Problem Related to Wastewater Treatment
• Adaptive Finite Element Methods for Optimal Control of Partial Differential Equations: Basic Concept
• A priori and a posteriori error estimates of H¹‐Galerkin mixed finite element method for parabolic optimal control problems
• Error estimates for finite element approximations of parabolic equations with measure data
• New development in freefem++
• Galerkin Finite Element Methods for Parabolic Problems
• A Priori Error Analysis for Finite Element Approximation of Parabolic Optimal Control Problems with Pointwise Control
• The Ritz–Galerkin Procedure for Parabolic Control Problems
• A posteriori error estimates for distributed convex optimal control problems