Stochastic discontinuous Galerkin methods for robust deterministic control of convection-diffusion equations with uncertain coefficients

Date

2023-04-01

Author

Çiloğlu, Pelin
Yücel, Hamdullah

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We investigate a numerical behavior of robust deterministic optimal control problem subject to a convection-diffusion equation containing uncertain inputs. Stochastic Galerkin approach, turning the original optimization problem containing uncertainties into a large system of deterministic problems, is applied to discretize the stochastic domain, while a discontinuous Galerkin method is preferred for the spatial discretization due to its better convergence behavior for optimization problems governed by convection dominated PDEs. Error analysis is done for the state and adjoint variables in the energy norm, while the estimate of deterministic control is obtained in the L2-norm. Large matrix system emerging from the stochastic Galerkin method is addressed by the low-rank version of GMRES method, which reduces both the computational complexity and the memory requirements by employing Kronecker-product structure of the obtained linear system. Benchmark examples with and without control constraints are presented to illustrate the efficiency of the proposed methodology.

URI

https://hdl.handle.net/11511/102233

Journal

ADVANCES IN COMPUTATIONAL MATHEMATICS

DOI

https://doi.org/10.1007/s10444-023-10015-5

Collections

Graduate School of Applied Mathematics, Article

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Citation Formats

P. Çiloğlu and H. Yücel, “Stochastic discontinuous Galerkin methods for robust deterministic control of convection-diffusion equations with uncertain coefficients,” ADVANCES IN COMPUTATIONAL MATHEMATICS, vol. 49, pp. 16–16, 2023, Accessed: 00, 2023. [Online]. Available: https://hdl.handle.net/11511/102233.