Goal–oriented a posteriori error estimation for Dirichlet boundary control problems

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10.1016:j.cam.2020.113012.pdf

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2021-1

Author

Yücel, Hamdullah

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We study goal-oriented a posteriori error estimates for the numerical approximation ofDirichlet boundary control problem governed by a convection diffusion equation withpointwise control constraints on a two dimensional convex polygonal domain. The localdiscontinuous Galerkin method is used as a discretization technique since the controlvariable is involved in a variational form in a natural sense. We derive primal–dualweightederrorestimatesfortheobjectivefunctionalwithanerrortermrepresentingthemismatch in the complementary system due to the discretization. Numerical examplesare presented to illustrate the performance of the proposed estimator.

Subject Keywords

Applied Mathematics, Computational Mathematics, Dirichlet boundary optimal control, Local discontinuous Galerkin, Goal–oriented adaptivity, A posteriori error estimate, Convection diffusion equation

URI

https://hdl.handle.net/11511/50722

Journal

Journal of Computational and Applied Mathematics

DOI

https://doi.org/10.1016/j.cam.2020.113012

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Graduate School of Applied Mathematics, Article

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Citation Formats

H. Yücel, “Goal–oriented a posteriori error estimation for Dirichlet boundary control problems,” Journal of Computational and Applied Mathematics, 2021, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/50722.