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Finite element error estimates for an optimal control problem governed by the Burgers equation

Listed author(s):
  • Pedro Merino

    ()

    (Escuela Politécnica Nacional)

Registered author(s):

    Abstract We derive a-priori error estimates for the finite-element approximation of a distributed optimal control problem governed by the steady one-dimensional Burgers equation with pointwise box constraints on the control. Here the approximation of the state and the control is done by using piecewise linear functions. With this choice, a superlinear order of convergence for the control is obtained in the $$L^2$$ L 2 -norm; moreover, under a further assumption on the regularity structure of the optimal control this error estimate can be improved to $$h^{3/2}$$ h 3 / 2 , extending the results in Rösch (Optim. Methods Softw. 21(1): 121–134, 2006). The theoretical findings are tested experimentally by means of numerical examples.

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    File URL: http://link.springer.com/10.1007/s10589-015-9790-0
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    Article provided by Springer in its journal Computational Optimization and Applications.

    Volume (Year): 63 (2016)
    Issue (Month): 3 (April)
    Pages: 793-824

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    Handle: RePEc:spr:coopap:v:63:y:2016:i:3:d:10.1007_s10589-015-9790-0
    DOI: 10.1007/s10589-015-9790-0
    Contact details of provider: Web page: http://www.springer.com

    Order Information: Web: http://www.springer.com/math/journal/10589

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