ADAPTIVE SYMMETRIC INTERIOR PENALTY GALERKIN METHOD FOR BOUNDARY CONTROL PROBLEMS

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2017-01-01

Author

BENNER, Peter
Yücel, Hamdullah

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We investigate an a posteriori error analysis of adaptive finite element approximations of linear-quadratic boundary optimal control problems under bilateral box constraints, which act on a Neumann boundary control. We use a symmetric interior Galerkin method as discretization technique. An efficient and reliable residual-type error estimator is introduced by invoking data oscillations. We then derive local upper and lower a posteriori error estimates for the boundary control problem. Adaptive mesh refinement indicated by a posteriori error estimates is applied. Numerical results are presented to illustrate the performance of the adaptive finite element approximation.

Subject Keywords

A posteriori error analysis, Optimal boundary control problems, Control constraints, Adaptive finite element methods, Discontinuous Galerkin methods

URI

https://hdl.handle.net/11511/31898

Journal

SIAM JOURNAL ON NUMERICAL ANALYSIS

DOI

https://doi.org/10.1137/15m1034507

Collections

Graduate School of Applied Mathematics, Article

Citation Formats

P. BENNER and H. Yücel, “ADAPTIVE SYMMETRIC INTERIOR PENALTY GALERKIN METHOD FOR BOUNDARY CONTROL PROBLEMS,” SIAM JOURNAL ON NUMERICAL ANALYSIS, vol. 55, no. 2, pp. 1101–1133, 2017, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/31898.