2014/03/12 by Nikolaus von Daniels, von Daniels, Nikolaus, Michael Hinze +3 · 1 citation
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Contact Mechanics and Variational Inequalities #Differential Equations and Numerical Methods #FOS: Mathematics #Optimization and Control (math.OC)
paper · pdf · doi:10.48550/arxiv.1403.3010
openalex publication_date 2014/03/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider a control constrained parabolic optimal control problem and use\nvariational discretization for its time semi-discretization. The state equation\nis treated with a Petrov-Galerkin scheme using a piecewise constant Ansatz for\nthe state and piecewise linear, continuous test functions. This results in\nvariants of the Crank-Nicolson scheme for the state and the adjoint state.\nExploiting a superconvergence result we prove second order convergence in time\nof the error in the controls. Moreover, the piecewise linear and continuous\nparabolic projection of the discrete state on the dual time grid provides a\nsecond order convergent approximation of the optimal state without further\nnumerical effort. Numerical experiments confirm our analytical findings.\n