Space-time finite element methods for second-order hyperbolic equations
Computer Methods in Applied Mechanics and Engineering
A Dirichlet boundary control problem for the strongly damped wave equation
SIAM Journal on Control and Optimization
A continuous space-time finite element method for the wave equation
Mathematics of Computation
SIAM Journal on Control and Optimization
Semismooth Newton Methods for Operator Equations in Function Spaces
SIAM Journal on Optimization
The Primal-Dual Active Set Strategy as a Semismooth Newton Method
SIAM Journal on Optimization
Neumann Boundary Control of Hyperbolic Equations with Pointwise State Constraints
SIAM Journal on Control and Optimization
Adaptive Space-Time Finite Element Methods for Parabolic Optimization Problems
SIAM Journal on Control and Optimization
Constrained Dirichlet Boundary Control in $L^2$ for a Class of Evolution Equations
SIAM Journal on Control and Optimization
Adaptivity with Dynamic Meshes for Space-Time Finite Element Discretizations of Parabolic Equations
SIAM Journal on Scientific Computing
Efficient numerical solution of parabolic optimization problems by finite element methods
Optimization Methods & Software
Mathematics and Computers in Simulation
A minimum effort optimal control problem for the wave equation
Computational Optimization and Applications
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In this paper optimal control problems governed by the wave equation with control constraints are analyzed. Three types of control action are considered: distributed control, Neumann boundary control, and Dirichlet control, and proper functional analytic settings for them are discussed. For treating inequality constraints, semismooth Newton methods are discussed and their convergence properties are investigated. In the case of distributed and Neumann control, superlinear convergence is shown. For Dirichlet boundary control, superlinear convergence is proved for a strongly damped wave equation. For numerical realization, a space-time finite element discretization is discussed. Numerical examples illustrate the results.