Adaptive discontinuous Galerkin methods for state constrained optimal control problems governed by convection diffusion equations

Hamdullah Yücel () and Peter Benner ()

Computational Optimization and Applications, 2015, vol. 62, issue 1, 321 pages

Abstract: We study a posteriori error estimates for the numerical approximations of state constrained optimal control problems governed by convection diffusion equations, regularized by Moreau–Yosida and Lavrentiev-based techniques. The upwind Symmetric Interior Penalty Galerkin (SIPG) method is used as a discontinuous Galerkin (DG) discretization method. We derive different residual-based error indicators for each regularization technique due to the regularity issues. An adaptive mesh refinement indicated by a posteriori error estimates is applied. Numerical examples are presented to illustrate the effectiveness of the adaptivity for both regularization techniques. Copyright Springer Science+Business Media New York 2015

Keywords: Optimal control problem; State constraints; Discontinuous Galerkin methods; Convection diffusion equations; A posteriori error estimates (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1007/s10589-014-9691-7

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