Journal of Computational Physics
SIAM Journal on Control and Optimization
Semismooth Newton Methods for Optimal Control of the Wave Equation with Control Constraints
SIAM Journal on Control and Optimization
Journal of Computational and Applied Mathematics
Computational Optimization and Applications
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Optimal Dirichlet boundary control based on the very weak solution of a parabolic state equation is analyzed. This approach allows us to consider the boundary controls in $L^2$, which has advantages over approaches which consider control in Sobolev spaces involving (fractional) derivatives. Pointwise constraints on the boundary are incorporated by the primal-dual active set strategy. Its global and local superlinear convergences are shown. A discretization based on space-time finite elements is proposed and numerical examples are included.