A priori error estimates for optimal control problems governed by the transient Stokes equations and subject to state constraints pointwise in time
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866917510363742208 |
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| author | Leykekhman, Dmitriy Vexler, Boris Wagner, Jakob |
| author_facet | Leykekhman, Dmitriy Vexler, Boris Wagner, Jakob |
| contents | In this paper, we consider a state constrained optimal control problem governed by the transient Stokes equations. The state constraint is given by an L2 functional in space, which is required to fulfill a pointwise bound in time. The discretization scheme for the Stokes equations consists of inf-sup stable finite elements in space and a discontinuous Galerkin method in time, for which we have recently established best approximation type error estimates. Using these error estimates, for the discrete control problem we establish error estimates and as a by-product we show an improved regularity for the optimal control. We complement our theoretical analysis with numerical results. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2407_20702 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A priori error estimates for optimal control problems governed by the transient Stokes equations and subject to state constraints pointwise in time Leykekhman, Dmitriy Vexler, Boris Wagner, Jakob Numerical Analysis Optimization and Control 49M41, 65M60, 49M25 In this paper, we consider a state constrained optimal control problem governed by the transient Stokes equations. The state constraint is given by an L2 functional in space, which is required to fulfill a pointwise bound in time. The discretization scheme for the Stokes equations consists of inf-sup stable finite elements in space and a discontinuous Galerkin method in time, for which we have recently established best approximation type error estimates. Using these error estimates, for the discrete control problem we establish error estimates and as a by-product we show an improved regularity for the optimal control. We complement our theoretical analysis with numerical results. |
| title | A priori error estimates for optimal control problems governed by the transient Stokes equations and subject to state constraints pointwise in time |
| topic | Numerical Analysis Optimization and Control 49M41, 65M60, 49M25 |
| url | https://arxiv.org/abs/2407.20702 |