Related papers: Error estimates for an unregularized optimal contr…
In this article, we investigate the stabilizability of the two- and three-dimensional Navier-Stokes equations with memory effects around a non-constant steady state using a localized interior control. The system is first linearized around a…
In this paper we study existence, dependence and optimal control results concerning solutions to a class of hemivariational inequalities for stationary Navier-Stokes equations but without making use of the theory of pseudo-monotone…
We consider bilinear optimal control problems, whose objective functionals do not depend on the controls. Hence, bang-bang solutions will appear. We investigate sufficient second-order conditions for bang-bang controls, which guarantee…
We consider optimal control problems of systems governed by stationary, incompressible generalized Navier-Stokes equations with shear dependent viscosity in a two-dimensional or three-dimensional domain. We study a general class of…
Error estimates with optimal convergence orders are proved for a stabilized Lagrange-Galerkin scheme for the Navier-Stokes equations. The scheme is a combination of Lagrange-Galerkin method and Brezzi-Pitkaranta's stabilization method. It…
We propose and analyze reliable and efficient a posteriori error estimators for an optimal control problem that involves a nondifferentiable cost functional, the Poisson problem as state equation and control constraints. To approximate the…
In this paper, we carry out the error analysis for the structure-preserving discretization of the incompressible MHD system. This system, as a coupled system of Navier-Stokes equations and Maxwell's equations, is nonlinear. We use its…
This work is concerned with optimal control problems where the objective functional consists of a tracking-type functional and an additional "multibang" regularization functional that promotes optimal control taking values from a given…
We consider an optimal control problem on a bounded domain $\Omega\subset\mathbb{R}^2,$ governed by a parabolic convection--diffusion--reaction equation with pointwise control constraints. We follow the optimize--then--discretize approach,…
We consider Tikhonov regularization of control-constrained optimal control problems. We present new a-priori estimates for the regularization error assuming measure and source-measure conditions. In the special case of bang-bang solutions,…
Discretization of Navier-Stokes' equations using pressure-robust finite element methods is considered for the high Reynolds number regime. To counter oscillations due to dominating convection we add a stabilization based on a bulk term in…
In this paper, we construct novel first- and second-order decoupled schemes for the Navier-Stokes equations based on the penalty method and the sequential regularization method (SRM), respectively. These schemes do not require the boundary…
The aim of this work is to present a model reduction technique in the framework of optimal control problems for partial differential equations. We combine two approaches used for reducing the computational cost of the mathematical numerical…
This paper is concerned with adaptive mesh refinement strategies for the spatial discretization of parabolic problems with dynamic boundary conditions. This includes the characterization of inf-sup stable discretization schemes for a…
A general a posteriori error analysis applies to five lowest-order finite element methods for two fourth-order semi-linear problems with trilinear non-linearity and a general source. A quasi-optimal smoother extends the source term to the…
In this paper, we discuss the numerical approximation of a distributed optimal control problem governed by the von Karman equations, defined in polygonal domains with point-wise control constraints. Conforming finite elements are employed…
We consider an optimal control problem subject to the thin-film equation which is deduced from the Navier--Stokes equation. The PDE constraint lacks well-posedness for general right-hand sides due to possible degeneracies; state constraints…
This paper deals with partially-observed optimal control problems for the state governed by stochastic differential equation with delay. We develop a stochastic maximum principle for this kind of optimal control problems using a variational…
The pressure correction scheme is combined with interior penalty discontinuous Galerkin method to solve the time-dependent Navier-Stokes equations. Optimal error estimates are derived for the velocity in the L$^2$ norm in time and in space.…
This article discusses numerical analysis of the distributed optimal control problem governed by the von K\'{a}rm\'{a}n equations defined on a polygonal domain in $\mathbb{R}^2$. The state and adjoint variables are discretised using the…