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A posteriori error estimates are obtained for both the state and the control approximations.
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My other projects include games and stochastic control problems on graphs, numerical homogenization, multi-objective and randomly-terminated optimal control, approximation of invariant manifolds of delay-differential equations, fast methods for constructing multi-valued solutions of PDEs, and dimension reduction in the context of chemical kinetics.
We derive a posteriori error estimates for the coupled state and control approximation.
We derive a posteriori error estimates for the state and control approximation.
Then, we derive a posteriori error estimates for both the state and the control approximation in Section 3.
Then equivalent a posteriori error estimators with lower and upper bounds for both state and control approximation are derived.
We derive a posteriori error estimates in L 2 ( J ; H 1 -norm and L 2 ( J ; L 2 -norm for both the coupled state and control approximation.
We have obtained some error estimate results for both the state, the co-state and the control approximation with convergence order hk+1.
We derive a posteriori error estimates in L ∞ ( J ; L 2 -norm and L 2 ( J ; L 2 -norm for both the state and the control approximation.
First of all, we use the (L^{2}) norm for estimating the control approximation error on the boundary, and the (H^{1}) norm for the state and co-state approximation error on the domain.
Then we also obtain sharper a posteriori error estimates for the control approximation and error estimates in the (L^{2}) norm for the state and co-state on the boundary.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com