Error estimate for indirect spectral approximation of optimal control problem governed by fractional diffusion equation with variable diffusivity coefficient (Q822170)
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scientific article; zbMATH DE number 7398298
| Language | Label | Description | Also known as |
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| English | Error estimate for indirect spectral approximation of optimal control problem governed by fractional diffusion equation with variable diffusivity coefficient |
scientific article; zbMATH DE number 7398298 |
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Error estimate for indirect spectral approximation of optimal control problem governed by fractional diffusion equation with variable diffusivity coefficient (English)
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21 September 2021
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The numerical solution of an optimal control problem is investigated, which has a space-fractional diffusion equation with variable diffusivity as a constraint. First-order optimality conditions are derived and the regularity of the solution of the optimality system is analyzed. An indirect spectral discrete scheme of the control problem is constructed and a priori error estimates of this scheme in weighted norms are derived. Numerical examples are presented which show the convergence rates of the proposed method.
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fractional diffusion equation
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optimal control
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Jacobi polynomials
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indirect spectral method
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variable coefficient
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