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• W3046256127 abstract "<p style='text-indent:20px;'>This paper aims at investigating the convergence and quasi- optimality of an adaptive finite element method for control constrained nonlinear elliptic optimal control problems. We derive a posteriori error estimation for both the control, the state and adjoint state variables under controlling by <inline-formula><tex-math id=M2>$ L^2 $</tex-math></inline-formula>-norms where bubble function is a wonderful tool to deal with the global lower error bound. Then a contraction is proved before the convergence is proposed. Furthermore, we find that if keeping the grids sufficiently mildly graded, we can prove the optimal convergence and the quasi-optimality for the adaptive finite element method. In addition, some numerical results are presented to verify our theoretical analysis.</p>" @default.
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• W3046256127 date "2020-01-01" @default.
• W3046256127 modified "2023-10-16" @default.
• W3046256127 title "Convergence and quasi-optimality of L^2- norms based an adaptive finite element method for nonlinear optimal control problems" @default.
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• W3046256127 doi "https://doi.org/10.3934/era.2020077" @default.
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