Error Estimates for the Numerical Approximation of Dirichlet Boundary Control for Semilinear Elliptic Equations
From MaRDI portal
Publication:3593007
DOI10.1137/050626600zbMath1123.65061OpenAlexW2041304886MaRDI QIDQ3593007
Eduardo Casas, Jean-Pierre Raymond
Publication date: 24 September 2007
Published in: SIAM Journal on Control and Optimization (Search for Journal in Brave)
Full work available at URL: http://hdl.handle.net/10902/1889
optimal controlerror estimatesfinite elementsnumerical examplessemilinear elliptic equationnumerical approximationDirichlet control
Numerical optimization and variational techniques (65K10) Newton-type methods (49M15) Existence theories for optimal control problems involving partial differential equations (49J20)
Related Items
Optimal control of perfect plasticity. I: stress tracking, A posteriori error estimates for semilinear optimal control problems, Finite Element Analysis of a Constrained Dirichlet Boundary Control Problem Governed by a Linear Parabolic Equation, Optimal Dirichlet control of partial differential equations on networks, A high accuracy NFEM for constrained optimal control problems governed by elliptic equations, Error Estimates for Approximate Solutions to Seminlinear Elliptic Optimal Control Problems with Nonlinear and Mixed Constraints, Continuity regularity of optimal control solutions to distributed and boundary semilinear elliptic optimal control problems with mixed pointwise control-state constraints, Finite element approximation of time fractional optimal control problem with integral state constraint, POD a-posteriori error estimates for linear-quadratic optimal control problems, Error estimates for finite element approximation of Dirichlet boundary control for Stokes equations in \(\mathbf{L}^2(\Gamma)\), On the Regularity of the Solutions of Dirichlet Optimal Control Problems in Polygonal Domains, Finite Element Approximation of Elliptic Dirichlet Optimal Control Problems, A Review of Numerical Analysis for the Discretization of the Velocity Tracking Problem, Weak boundary penalization for Dirichlet boundary control problems governed by elliptic equations, Finite element method and a priori error estimates for Dirichlet boundary control problems governed by parabolic PDEs, Error Estimates for a Pointwise Tracking Optimal Control Problem of a Semilinear Elliptic Equation, Using piecewise linear functions in the numerical approximation of semilinear elliptic control problems, A New HDG Method for Dirichlet Boundary Control of Convection Diffusion PDEs II: Low Regularity, Numerical analysis for the pure Neumann control problem using the gradient discretisation method, Unnamed Item, Nitsche's method for elliptic Dirichlet boundary control problems on curved domains, A two level finite element method for Stokes constrained Dirichlet boundary control problem, Finite element approximation to optimal Dirichlet boundary control problem: a priori and a posteriori error estimates, Superconvergence analysis of a nonconforming finite element method for monotone semilinear elliptic optimal control problems, Analysis and approximations of an optimal control problem for the Allen-Cahn equation, Numerical analysis of a family of simultaneous distributed-boundary mixed elliptic optimal control problems and their asymptotic behaviour through a commutative diagram and error estimates, Unified discontinuous Galerkin finite element methods for second order Dirichlet boundary control problem, Error estimates of Fourier finite volume element method for parabolic Dirichlet boundary optimal control problems on complex connected domains, Convergence and quasi-optimality of an adaptive finite element method for elliptic Robin boundary control problem, High accuracy analysis of nonconforming MFEM for constrained optimal control problems governed by Stokes equations, Goal-oriented a posteriori error estimation for Dirichlet boundary control problems, Discretization of Optimal Control Problems, Analysis and Approximations of Dirichlet Boundary Control of Stokes Flows in the Energy Space, Optimal control of lake eutrophication, Error analysis for the finite element approximations of Dirichlet parabolic boundary control problem with measure data, Boundary concentrated finite elements for optimal boundary control problems of elliptic PDEs, Error bounds for a Dirichlet boundary control problem based on energy spaces, Mixed finite element method for a second order Dirichlet boundary control problem, FEM for semilinear elliptic optimal control with nonlinear and mixed constraints, Error estimates for Dirichlet control problems in polygonal domains: quasi-uniform meshes, A finite element method for elliptic Dirichlet boundary control problems, A parabolic inverse convection-diffusion-reaction problem solved using space-time localization and adaptivity, An Error Analysis of Discontinuous Finite Element Methods for the Optimal Control Problems Governed by Stokes Equation, Solving ill-posed control problems by stabilized finite element methods: an alternative to Tikhonov regularization, Optimal Control of Partial Differential Equations, Adaptive finite element method for Dirichlet boundary control of elliptic partial differential equations, A posteriori error estimates for parabolic optimal control problems with controls acting on lower dimensional manifolds, On linear-quadratic elliptic control problems of semi-infinite type, Optimization methods for Dirichlet control problems, A \(C^0\) interior penalty method for the Dirichlet control problem governed by biharmonic operator, Nonconforming finite element methods for the constrained optimal control problems governed by nonsmooth elliptic equations, On the Error Estimates for the Finite Element Approximation of a Class of Boundary Optimal Control Systems, A nonconforming finite element method for constrained optimal control problems governed by parabolic equations, An optimal osmotic control problem for a concrete dam system, Error estimates for the numerical approximation of Neumann control problems governed by a class of quasilinear elliptic equations, A general theorem on error estimates with application to a quasilinear elliptic optimal control problem, Approximation of sparse controls in semilinear equations by piecewise linear functions, Two fast finite difference schemes for elliptic Dirichlet boundary control problems, An energy space finite element approach for elliptic Dirichlet boundary control problems, Meshless methods for solving Dirichlet boundary optimal control problems governed by elliptic PDEs, Discrete concepts versus error analysis in PDE-constrained optimization, A FrameWork for the Error Analysis of Discontinuous Finite Element Methods for Elliptic Optimal Control Problems and Applications toC0IP Methods, Boundary element methods for Dirichlet boundary control problems, Finite element methods for elliptic optimal control problems with boundary observations, Finite Element Approximations of Parabolic Optimal Control Problems with Controls Acting on a Lower Dimensional Manifold, A superconvergent hybridizable discontinuous Galerkin method for Dirichlet boundary control of elliptic PDEs, Error estimates for variational normal derivatives and Dirichlet control problems with energy regularization, Discretization of optimal control problems governed by \(p\)-Laplacian elliptic equations, Sparse Dirichlet optimal control problems, Fourier Finite Volume Element Method for Two Classes of Optimal Control Problems Governed by Elliptic PDEs on Complex Connected Domain, Explicit solutions for distributed, boundary and distributed-boundary elliptic optimal control problems, Numerical approximation of control problems of non-monotone and non-coercive semilinear elliptic equations, Discretization of the Poisson equation with non-smooth data and emphasis on non-convex domains, Optimal Control of the Inhomogeneous Relativistic Maxwell--Newton--Lorentz Equations, Adapted Numerical Methods for the Poisson Equation with $L^2$ Boundary Data in NonConvex Domains, Penalization of Dirichlet optimal control problems, An HDG Method for Dirichlet Boundary Control of Convection Dominated Diffusion PDEs, Finite Element Error Estimates for Normal Derivatives on Boundary Concentrated Meshes, Analysis of a hybridizable discontinuous Galerkin scheme for the tangential control of the Stokes system, On Discrete Shape Gradients of Boundary Type for PDE-constrained Shape Optimization, A multi-mode expansion method for boundary optimal control problems constrained by random Poisson equations, A note on the approximation of Dirichlet boundary control problems for the wave equation on curved domains, A class of embedded DG methods for Dirichlet boundary control of convection diffusion PDEs, Finite element analysis of the constrained Dirichlet boundary control problem governed by the diffusion problem, Error estimates for the discretization of the velocity tracking problem, PDE-constrained optimal control approach for the approximation of an inverse Cauchy problem, Dirichlet control of elliptic state constrained problems
