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Article

MSC: 49J20, 65N30
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Keywords:
a posteriori error estimate; general optimal control problem; nonlinear parabolic equation; mixed finite element method
Summary:
We study new a posteriori error estimates of the mixed finite element methods for general optimal control problems governed by nonlinear parabolic equations. The state and the co-state are discretized by the high order Raviart-Thomas mixed finite element spaces and the control is approximated by piecewise constant functions. We derive a posteriori error estimates in $L^{\infty }(J;L^2(\Omega )) $-norm and $L^2(J;L^2(\Omega ))$-norm for both the state, the co-state and the control approximation. Such estimates, which seem to be new, are an important step towards developing a reliable adaptive mixed finite element approximation for optimal control problems. Finally, the performance of the posteriori error estimators is assessed by two numerical examples.
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