Numerical solutions for optimal control problem governed by elliptic system on Lipschitz domains

What is it about?

In this paper, an optimal boundary control problem for a distributed elliptic system on Lipschitz domains with boundary homogeneous Dirichlet conditions and independently with Neumann conditions is analyzed. The necessary and sufficient optimality conditions for such problems with the quadratic cost functionals are obtained. A Jacobi spectral Galerkin method is introduced to develop a direct solution technique for the numerical solution of elliptic problems subject to Dirichlet and Neumann conditions in one and two dimensions. The numerical examples are included to demonstrate the validity and applicability of the techniques and comparison is made with the existing results. The method is easy to implement and yields very accurate results.

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Why is it important?

We give some new results for an optimal boundary control problem for a distributed elliptic system on Lipschitz domains with boundary homogeneous Dirichlet conditions and independently with Neumann conditions The necessary and sufficient optimality conditions for such problems with the quadratic cost functionals are obtained. A Jacobi spectral Galerkin method is introduced to develop a direct solution technique for the numerical solution of elliptic problems subject to Dirichlet and Neumann conditions in one and two dimensions. The numerical examples are included to demonstrate the validity and applicability of the techniques and comparison is made with the existing results. The method is easy to implement and yields very accurate results.

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