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

Pedro Merino ()

Computational Optimization and Applications, 2016, vol. 63, issue 3, 793-824

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

Keywords: Optimal control; Burgers equation; Finite element approximation; Piecewise linear; Error estimates; 35Q53; 49K20; 49J20; 80M10; 49N05; 65N12; 41A25 (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/s10589-015-9790-0

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