A priori error estimates for optimal control problems governed by the transient Stokes equations and subject to state constraints pointwise in time
Provides rigorous error analysis for a class of PDE-constrained optimization problems, benefiting researchers in computational optimal control and fluid dynamics.
The paper derives a priori error estimates for optimal control problems governed by transient Stokes equations with pointwise-in-time state constraints, using inf-sup stable finite elements and discontinuous Galerkin time discretization. Numerical results confirm the theoretical findings.
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.