Divergence conforming DG method for the optimal control of the Oseen equation with variable viscosity
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866909586999476224 |
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| author | Singh, Harpal Khan, Arbaz |
| author_facet | Singh, Harpal Khan, Arbaz |
| contents | This study introduces the divergence-conforming discontinuous Galerkin finite element method (DGFEM) for numerically approximating optimal control problems with distributed constraints, specifically those governed by stationary generalized Oseen equations. We provide optimal a priori error estimates in energy norms for such problems using the divergence-conforming DGFEM approach. Moreover, we thoroughly analyze $L^2$ error estimates for scenarios dominated by diffusion and convection. Additionally, we establish the new reliable and efficient a posteriori error estimators for the optimal control of the Oseen equation with variable viscosity. Theoretical findings are validated through numerical experiments conducted in both two and three dimensions. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2403_15783 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Divergence conforming DG method for the optimal control of the Oseen equation with variable viscosity Singh, Harpal Khan, Arbaz Numerical Analysis Optimization and Control 49K20, 49N10, 65N12, 65N30, 76M10 This study introduces the divergence-conforming discontinuous Galerkin finite element method (DGFEM) for numerically approximating optimal control problems with distributed constraints, specifically those governed by stationary generalized Oseen equations. We provide optimal a priori error estimates in energy norms for such problems using the divergence-conforming DGFEM approach. Moreover, we thoroughly analyze $L^2$ error estimates for scenarios dominated by diffusion and convection. Additionally, we establish the new reliable and efficient a posteriori error estimators for the optimal control of the Oseen equation with variable viscosity. Theoretical findings are validated through numerical experiments conducted in both two and three dimensions. |
| title | Divergence conforming DG method for the optimal control of the Oseen equation with variable viscosity |
| topic | Numerical Analysis Optimization and Control 49K20, 49N10, 65N12, 65N30, 76M10 |
| url | https://arxiv.org/abs/2403.15783 |