Optimal finite element error estimates for an optimal control problem governed by the wave equation with controls of bounded variation
| Autor: | Philip Trautmann, Sebastian Engel, Boris Vexler |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
0209 industrial biotechnology
Applied Mathematics General Mathematics 010102 general mathematics Mathematical analysis Numerical Analysis (math.NA) 02 engineering and technology Optimal control Wave equation 01 natural sciences Finite element method 26A45 49J20 49M25 65N15 65N30 Computational Mathematics 020901 industrial engineering & automation Optimization and Control (math.OC) Bounded variation FOS: Mathematics Mathematics - Numerical Analysis 0101 mathematics Mathematics - Optimization and Control Mathematics |
| Zdroj: | IMA Journal of Numerical Analysis |
| Popis: | This work discusses the finite element discretization of an optimal control problem for the linear wave equation with time-dependent controls of bounded variation. The main focus lies on the convergence analysis of the discretization method. The state equation is discretized by a space-time finite element method. The controls are not discretized. Under suitable assumptions optimal convergence rates for the error in the state and control variable are proven. Based on a conditional gradient method the solution of the semi-discretized optimal control problem is computed. The theoretical convergence rates are confirmed in a numerical example. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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