Computational Optimization and Applications

, Volume 63, Issue 3, pp 793–824 | Cite as

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

  • Pedro MerinoEmail author


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 \(L^2\)-norm; moreover, under a further assumption on the regularity structure of the optimal control this error estimate can be improved to \(h^{3/2}\), extending the results in Rösch (Optim. Methods Softw. 21(1): 121–134, 2006). The theoretical findings are tested experimentally by means of numerical examples.


Optimal control Burgers equation Finite element approximation Piecewise linear Error estimates 

Mathematics Subject Classification

35Q53 49K20 49J20 80M10 49N05 65N12 41A25 


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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.ModeMat: Research Center on Mathematical Modeling, Departamento de MatemáticaEscuela Politécnica NacionalQuitoEcuador

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