Weak boundary penalization for Dirichlet boundary control problems governed by elliptic equations

DOI10.1016/j.jmaa.2017.04.016zbMath1365.65169OpenAlexW2607227185MaRDI QIDQ2396883

Wei Gong, Lili Chang, Ning-Ning Yan

Publication date: 26 May 2017

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2017.04.016

zbMATH Keywords

finite element methodnumerical experimentDirichlet boundary controla priori error estimateweak boundary penalization

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 (6)

A New HDG Method for Dirichlet Boundary Control of Convection Diffusion PDEs II: Low Regularity ⋮ Nitsche's method for elliptic Dirichlet boundary control problems on curved domains ⋮ A finite element method for elliptic Dirichlet boundary control problems ⋮ Two fast finite difference schemes for elliptic Dirichlet boundary control problems ⋮ A superconvergent hybridizable discontinuous Galerkin method for Dirichlet boundary control of elliptic PDEs ⋮ Analysis of a hybridizable discontinuous Galerkin scheme for the tangential control of the Stokes system

Uses Software

• AFEPack

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Finite element methods with symmetric stabilization for the transient convection-diffusion-reaction equation
• Approximation of a class of optimal control problems with order of convergence estimates
• Error estimates for the numerical approximation of boundary semilinear elliptic control prob\-lems
• Error estimates for the numerical approximation of Neumann control problems
• Über ein Variationsprinzip zur Lösung von Dirichlet-Problemen bei Verwendung von Teilräumen, die keinen Randbedingungen unterworfen sind. (On a variational principle for solving Dirichlet problems less boundary conditions using subspaces)
• Finite element convergence for singular data
• A Posteriori Error Estimates for Convex Boundary Control Problems
• Error Analysis for a Finite Element Approximation of Elliptic Dirichlet Boundary Control Problems
• Approximation of Boundary Control Problems on Curved Domains
• Mixed Finite Element Method for Dirichlet Boundary Control Problem Governed by Elliptic PDEs
• Optimization with PDE Constraints
• Finite Element Approximation of Dirichlet Boundary Control for Elliptic PDEs on Two- and Three-Dimensional Curved Domains
• Error Estimates for the Numerical Approximation of Dirichlet Boundary Control for Semilinear Elliptic Equations
• Weighted error estimates of the continuous interior penalty method for singularly perturbed problems
• Penalization of Dirichlet optimal control problems
• On the approximation of the solution of an optimal control problem governed by an elliptic equation
• Some Optimal Error Estimates for Piecewise Linear Finite Element Approximations
• Singular perturbation for the Dirichlet boundary control of elliptic problems
• Approximations of Very Weak Solutions to Boundary-Value Problems
• The Mathematical Theory of Finite Element Methods
• On kernels, eigenvalues, and eigenfunctions of operators related to elliptic problems

This page was built for publication: Weak boundary penalization for Dirichlet boundary control problems governed by elliptic equations