A new approximation method for PDE constraint optimal control problem solutions
Résumé
In this article, we present a method to solve the optimal control with elliptic partial differential equation constraint, based on the new method of spectral element. In this new method, we use Müntez polynomials as interpolation polynomials. Using this method, we get the discrete form of the problem, which is itself a large scale constrained optimization problem. We use the split Bregman method to solve this optimization problem. In the end, we will check the accuracy and efficiency of the method with some numerical examples.
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