A priori error estimates for the finite element discretization of optimal distributed control problems governed by the biharmonic operator
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Publication:372881
DOI10.1007/s10092-012-0063-3zbMath1273.65164OpenAlexW2031770526MaRDI QIDQ372881
Winnifried Wollner, Rolf Rannacher, Stefan Frei
Publication date: 21 October 2013
Published in: Calcolo (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s10092-012-0063-3
Numerical optimization and variational techniques (65K10) Error bounds for boundary value problems involving PDEs (65N15) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30)
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Cites Work
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- Elliptic control problems with gradient constraints -- variational discrete versus piecewise constant controls
- Error estimates and superconvergence of mixed finite element methods for convex optimal control problems
- A priori error estimates for optimal control problems with pointwise constraints on the gradient of the state
- 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
- Finite element approximation of elliptic control problems with constraints on the gradient
- Convergence of approximations vs. regularity of solutions for convex, control-constrained optimal-control problems
- On mixed finite element methods in plate bending analysis. I: The first Herrmann scheme
- A variational discretization concept in control constrained optimization: The linear-quadratic case
- Error estimates for the numerical approximation of a semilinear elliptic control problem
- Uniform convergence of the FEM applications to state constrained control problems
- Error estimates of mixed finite element methods for quadratic optimal control problems
- Error estimates for linear-quadratic control problems with control constraints
- $L^\infty$-Estimates for Approximated Optimal Control Problems
- Convergence of a Finite Element Approximation to a State-Constrained Elliptic Control Problem
- Error estimates for the finite element approximation of a semilinear elliptic control problem with state constraints and finite dimensional control space
- Finite Element Approximation of Dirichlet Boundary Control for Elliptic PDEs on Two- and Three-Dimensional Curved Domains
- On nonconforming an mixed finite element methods for plate bending problems. The linear case
- On the approximation of the solution of an optimal control problem governed by an elliptic equation
- On the boundary value problem of the biharmonic operator on domains with angular corners
- A mixed method for 4th order problems using linear finite elements
- An Introduction to Variational Inequalities and Their Applications
- Superconvergence Properties of Optimal Control Problems
- Optimal Control of a Biharmonic Obstacle Problem
- Optimal Control of the Stokes Equations: A Priori Error Analysis for Finite Element Discretization with Postprocessing
- Numerical Analysis of a Control and State Constrained Elliptic Control Problem with Piecewise Constant Control Approximations
