ADAPTIVE SYMMETRIC INTERIOR PENALTY GALERKIN METHOD FOR BOUNDARY CONTROL PROBLEMS

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2017-01-01
BENNER, Peter
Yücel, Hamdullah
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.

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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.