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A priori error estimates for the finite element discretization of optimal distributed control problems governed by the biharmonic operator

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2013

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Rannacher, Rolf
Wollner, Winnifried

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https://doi.org/10.1007/s10092-012-0063-3
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Calcolo. Springer. 2013, 50, pp. 165-193. ISSN 0008-0624. eISSN 1126-5434. Available under: doi: 10.1007/s10092-012-0063-3

Zusammenfassung

In this article a priori error estimates are derived for the finite element discretization of optimal distributed control problems governed by the biharmonic operator. The state equation is discretized in primal mixed form using continuous piecewise biquadratic finite elements, while piecewise constant approximations are used for the control. The error estimates derived for the state variable as well as that for the control are order-optimal on general unstructured meshes. However, on uniform meshes not all error estimates are optimal due to the low-order control approximation. All theoretical results are confirmed by numerical tests.

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Fachgebiet (DDC)
510 Mathematik

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Optimal distributed control, Biharmonic operator, Mixed finite element method, A priori error estimates

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ISO 690FREI, Stefan, Rolf RANNACHER, Winnifried WOLLNER, 2013. A priori error estimates for the finite element discretization of optimal distributed control problems governed by the biharmonic operator. In: Calcolo. Springer. 2013, 50, pp. 165-193. ISSN 0008-0624. eISSN 1126-5434. Available under: doi: 10.1007/s10092-012-0063-3
BibTex
@article{Frei2013prior-55821,
  year={2013},
  doi={10.1007/s10092-012-0063-3},
  title={A priori error estimates for the finite element discretization of optimal distributed control problems governed by the biharmonic operator},
  volume={50},
  issn={0008-0624},
  journal={Calcolo},
  pages={165--193},
  author={Frei, Stefan and Rannacher, Rolf and Wollner, Winnifried}
}
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