A finite element method for elliptic optimal control problem on a non-convex polygon with corner singularities

DOI10.1016/j.camwa.2017.08.029zbMath1418.65168OpenAlexW2754188507MaRDI QIDQ2314269

Hyung Jun Choi, Woocheol Choi, Youngwoo Koh

Publication date: 22 July 2019

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.camwa.2017.08.029

zbMATH Keywords

corner singularitynon-convex polygonelliptic optimal control problem

Mathematics Subject Classification ID

Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Discrete approximations in optimal control (49M25)

Cites Work

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• 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
• Using piecewise linear functions in the numerical approximation of semilinear elliptic control problems
• Direct and inverse error estimates for finite elements with mesh refinements
• Convergence of approximations vs. regularity of solutions for convex, control-constrained optimal-control problems
• Elliptic boundary value problems on corner domains. Smoothness and asymptotics of solutions
• Multigrid methods for the computation of singular solutions and stress intensity factors. II: Crack singularities
• Error estimates for the numerical approximation of a semilinear elliptic control problem
• Error estimates for parabolic optimal control problems with control constraints
• A finite element method for computing accurate solutions for Poisson equations with corner singularities using the stress intensity factor
• On the use of singular functions with finite element approximations
• Optimal control in non-convex domains: a priori discretization error estimates
• A Finite Element Method Using Singular Functions for the Poisson Equation: Corner Singularities
• Solution Methods for the Poisson Equation with Corner Singularities: Numerical Results
• Local mesh refinement for the discretization of Neumann boundary control problems on polyhedra
• Graded Meshes in Optimal Control for Elliptic Partial Differential Equations: An Overview
• Maximum Norm Estimates in the Finite Element Method on Plane Polygonal Domains. Part 2, Refinements
• Error estimates for linear-quadratic control problems with control constraints
• $L^\infty$-Estimates for Approximated Optimal Control Problems
• On the Regularity of the Solutions of Dirichlet Optimal Control Problems in Polygonal Domains
• Error estimates on the coeficients obtained by the singular function method
• Finite Element Methods for Navier-Stokes Equations
• On the approximation of the solution of an optimal control problem governed by an elliptic equation
• Coefficients of the Singularities for Elliptic Boundary Value Problems on Domains with Conical Points. III: Finite Element Methods on Polygonal Domains
• An Observation Concerning Ritz-Galerkin Methods with Indefinite Bilinear Forms
• Singularities in the Solution of Laplace's Equation in Two Dimensions
• Maximum Norm Estimates in the Finite Element Method on Plane Polygonal Domains. Part 1
• Multigrid methods for the computation of singular solutions and stress intensity factors I: Corner singularities
• Finite element error estimates on the boundary with application to optimal control

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