相关论文: A posteriori error analysis for a distributed opti…
We derive a-priori error estimates for the finite-element approximation of a distributed optimal control problem governed by the steady one-dimensional Burgers equation with pointwise box constraints on the control. Here the approximation…
This paper considers the finite element approximation to parabolic optimal control problems with measure data in a nonconvex polygonal domain. Such problems usually possess low regularity in the state variable due to the presence of measure…
In this work, we present numerical analysis for a distributed optimal control problem, with box constraint on the control, governed by a subdiffusion equation which involves a fractional derivative of order $\alpha\in(0,1)$ in time. The…
In this paper, we investigate an optimal control problem governed by parabolic equations with measure-valued controls over time. We establish the well-posedness of the optimal control problem and derive the first-order optimality condition…
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…
We consider an optimal control problem governed by an elliptic variational inequality of the second kind. The problem is discretized by linear finite elements for the state and a variational discrete approach for the control. Based on a…
We consider control constrained optimal control problems governed by parameterized stationary Maxwell's system with the Gauss's law. The parameters enter through dielectric, magnetic permeability, and charge density. Moreover, the parameter…
In this paper we present and analyze a weighted residual a posteriori error estimate for an optimal control problem. The problem involves a nondifferentiable cost functional, a state equation with an integral fractional Laplacian, and…
We analyze a bilinear optimal control problem for the Stokes--Brinkman equations: the control variable enters the state equations as a coefficient. In two- and three-dimensional Lipschitz domains, we perform a complete continuous analysis…
This work focuses on numerical solutions of optimal control problems. A time discretization error representation is derived for the approximation of the associated value function. It concerns Symplectic Euler solutions of the Hamiltonian…
We provide a framework for the numerical approximation of distributed optimal control problems, based on least-squares finite element methods. Our proposed method simultaneously solves the state and adjoint equations and is $\inf$--$\sup$…
In this paper, an abstract framework for the error analysis of discontinuous finite element method is developed for the distributed and Neumann boundary control problems governed by the stationary Stokes equation with control constraints.…
In this paper we consider a parabolic optimal control problem with a Dirac type control with moving point source in two space dimensions. We discretize the problem with piecewise constant functions in time and continuous piecewise linear…
In this paper we investigate a priori error estimates for the space-time Galerkin finite element discretization of an optimal control problem governed by a simplified linear gradient enhanced damage model. The model equations are of a…
A posteriori error estimates are an important tool to bound discretization errors in terms of computable quantities avoiding regularity conditions that are often difficult to establish. For non-linear and non-differentiable problems,…
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…
This work reviews goal-oriented a posteriori error control, adaptivity and solver control for finite element approximations to boundary and initial-boundary value problems for stationary and non-stationary partial differential equations,…
This paper focuses on a posteriori error estimates for a pressure-robust finite element method, which incorporates a divergence-free reconstruction operator, within the context of the distributed optimal control problem constrained by the…
This work presents the multiharmonic analysis and derivation of functional type a posteriori estimates of a distributed eddy current optimal control problem and its state equation in a time-periodic setting. The existence and uniqueness of…
We consider an unregularized optimal control problem subject to the steady-state Navier-Stokes equations. We derive the existence of optimal solutions and prove first- and second-order optimality conditions. To approximate solutions to the…