A FrameWork for the Error Analysis of Discontinuous Finite Element Methods for Elliptic Optimal Control Problems and Applications toC0IP Methods

DOI10.1080/01630563.2015.1068182zbMath1336.65110arXiv1411.0796OpenAlexW1926947049MaRDI QIDQ2795095

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Publication date: 18 March 2016

Published in: Numerical Functional Analysis and Optimization (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1411.0796

zbMATH Keywords

optimal controladaptive mesh refinementbiharmonic equationdiscontinuous Galerkin methodnumerical experimenterror estimators

Mathematics Subject Classification ID

Numerical optimization and variational techniques (65K10) Existence theories for optimal control problems involving partial differential equations (49J20) Discrete approximations in optimal control (49M25)

Related Items (10)

Global superconvergence analysis of a nonconforming FEM for Neumann boundary OCPs with elliptic equations ⋮ Variational and virtual discretizations of optimal control problems governed by diffusion problems ⋮ Finite Element Analysis of a Constrained Dirichlet Boundary Control Problem Governed by a Linear Parabolic Equation ⋮ A posteriori error analysis for a distributed optimal control problem governed by the von Kármán equations ⋮ Unified discontinuous Galerkin finite element methods for second order Dirichlet boundary control problem ⋮ An adaptive \(\mathrm{C}^0\) Interior penalty discontinuous Galerkin method and an equilibrated a posteriori error estimator for the von Kármán equations ⋮ Error bounds for a Dirichlet boundary control problem based on energy spaces ⋮ An Error Analysis of Discontinuous Finite Element Methods for the Optimal Control Problems Governed by Stokes Equation ⋮ A \(C^0\) interior penalty method for the Dirichlet control problem governed by biharmonic operator ⋮ Finite element analysis of the constrained Dirichlet boundary control problem governed by the diffusion problem

Cites Work

• Unnamed Item
• Unnamed Item
• A priori error estimates for the finite element discretization of optimal distributed control problems governed by the biharmonic operator
• Convergence and optimality of the adaptive Morley element method
• Elliptic control problems with gradient constraints -- variational discrete versus piecewise constant controls
• \(C^0\) interior penalty methods for fourth order elliptic boundary value problems on polygonal domains
• A priori error estimates for optimal control problems with pointwise constraints on the gradient of the state
• Finite element error estimates for Neumann boundary control problems on graded meshes
• Ciarlet-Raviart mixed finite element approximation for an optimal control problem governed by the first bi-harmonic equation
• Approximation of a class of optimal control problems with order of convergence estimates
• A variational discretization concept in control constrained optimization: The linear-quadratic case
• Continuous/discontinuous finite element approximations of fourth-order elliptic problems in structural and continuum mechanics with applications to thin beams and plates, and strain gradient elasticity
• Analysis of an interior penalty method for fourth order problems on polygonal domains
• An energy space finite element approach for elliptic Dirichlet boundary control problems
• An interior penalty method for distributed optimal control problems governed by the biharmonic operator
• Error Analysis for a Finite Element Approximation of Elliptic Dirichlet Boundary Control Problems
• Discrete Reliability for Crouzeix--Raviart FEMs
• Divergence-Conforming Discontinuous Galerkin Methods and $C^0$ Interior Penalty Methods
• A $\mathcal{C}^0$ Interior Penalty Method for a Fourth Order Elliptic Singular Perturbation Problem
• An interior penalty method for a sixth-order elliptic equation
• A new error analysis for discontinuous finite element methods for linear elliptic problems
• A Quadratic $C^0$ Interior Penalty Method for Linear Fourth Order Boundary Value Problems with Boundary Conditions of the Cahn--Hilliard Type
• A Posteriori Error Analysis of Optimal Control Problems with Control Constraints
• Ana posteriorierror analysis of adaptive finite element methods for distributed elliptic control problems with control constraints
• Optimization with PDE Constraints
• An a posteriori error estimator for a quadratic C0-interior penalty method for the biharmonic problem
• Error Estimates for the Numerical Approximation of Dirichlet Boundary Control for Semilinear Elliptic Equations
• On the boundary value problem of the biharmonic operator on domains with angular corners
• Analysis and finite element approximation of optimal control problems for the stationary Navier-Stokes equations with Dirichlet controls
• The Primal-Dual Active Set Strategy as a Semismooth Newton Method
• Superconvergence Properties of Optimal Control Problems
• Poincaré–Friedrichs Inequalities for PiecewiseH²Functions
• A Convergent Adaptive Algorithm for Poisson’s Equation
• Error analysis of discontinuous Galerkin methods for the Stokes problem under minimal regularity
• The Mathematical Theory of Finite Element Methods

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