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

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  • Pedro Merino

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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. Copyright Springer Science+Business Media New York 2016

Suggested Citation

  • Pedro Merino, 2016. "Finite element error estimates for an optimal control problem governed by the Burgers equation," Computational Optimization and Applications, Springer, vol. 63(3), pages 793-824, April.
  • Handle: RePEc:spr:coopap:v:63:y:2016:i:3:p:793-824
    DOI: 10.1007/s10589-015-9790-0
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