A priori error estimates for optimal control problems governed by the transient Stokes equations and subject to state constraints pointwise in time
Year: 2025
Type: article
Abstract: In this paper, we consider a state constrained optimal control problem governed by the transient Stokes equations. The state constraint is given by an $L^{2}$ 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 derive error estimates and as a by-product we show an improved regularity for the optimal control. We complement our theoretical analysis with numerical results.
Authors: Dmitriy Leykekhman, Boris Vexler, Jakob Wagner
Institutions: University of Connecticut, Technical University of Munich
Language: English
Subfield: Computational Mechanics
Field: Engineering
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,718
OpenAlex ID: W4409396595