Finite element error analysis for measure-valued optimal control problems governed by a 1D wave equation with variable coefficients
| Autor: | Philip Trautmann, Boris Vexler, Alexander Zlotnik |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: |
Control and Optimization
010103 numerical & computational mathematics optimal control 01 natural sciences Measure (mathematics) Omega Regularization (mathematics) Combinatorics Quadratic equation Primary: 65M60 49K20 49M05 49M25 49M29 Secondary: 35L05 FOS: Mathematics Mathematics - Numerical Analysis 0101 mathematics Mathematics - Optimization and Control Mathematics Variable (mathematics) finite element method Computer Science::Information Retrieval Applied Mathematics 010102 general mathematics Numerical Analysis (math.NA) Term (logic) Wave equation stability Finite element method vector measure control Optimization and Control (math.OC) measure-valued control error estimates |
| DOI: | 10.3934/mcrf.2018017 |
| Popis: | This work is concerned with the optimal control problems governed by a 1D wave equation with variable coefficients and the control spaces $\mathcal M_T$ of either measure-valued functions $L_{w^*}^2(I,\mathcal M(\Omega))$ or vector measures $\mathcal M(\Omega,L^2(I))$. The cost functional involves the standard quadratic tracking terms and the regularization term $\alpha\|u\|_{\mathcal M_T}$ with $\alpha>0$. We construct and study three-level in time bilinear finite element discretizations for this class of problems. The main focus lies on the derivation of error estimates for the optimal state variable and the error measured in the cost functional. The analysis is mainly based on some previous results of the authors. The numerical results are included. Comment: 39 pages, 6 figures |
| Databáze: | OpenAIRE |
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