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The main results of this work state convergence and optimality of the adaptive algorithm in the sense that the error estimator converges with optimal convergence rate.
We show that our algorithm achieves the optimal convergence rate up to a logarithmic factor.
Numerical results validate our findings and indicate optimal convergence orders.
What we must do is work towards a context in which all legitimate interests, rights, and values are represented and can find their optimal convergence.
Numerical results show optimal convergence and robustness in handling very complex geometries.
The numerical analysis of the linearized problem also shows that the method has optimal convergence properties.
Moreover, optimal convergence rates in both L2 and discrete energy norms are proved.
Furthermore, based on different splitting terms, three unconditionally stable ADI compact schemes with optimal convergence order are developed respectively.
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The optimal convergence-control parameters can be determined by minimizing the averaged residual error.
The non-symmetric schemes lead to a cell energy/entropy inequality but exhibit sub-optimal convergence rates.
The adaptive wavelet threshold estimator with near-optimal convergence rate in a wide range of Besov scale is also constructed.
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