Error Estimates for Fractional Semilinear Optimal Control on Lipschitz Polytopes

A Posteriori Error Estimates for Semilinear Boundary Control Problems

In this paper we study the finite element approximation for boundary control problems governed by semilinear elliptic equations. Optimal control problems are very important model in science and engineering numerical simulation. They have various physical backgrounds in many practical applications. Finite element approximation of optimal control problems plays a very important role in the numeri...

A priori error estimates for state constrained semilinear parabolic optimal control problems

We consider the finite element discretization of semilinear parabolic optimization problems subject to pointwise in time constraints on mean values of the state variable. In contrast to many results in numerical analysis of optimization problems subject to semilinear parabolic equations, we assume weak second order sufficient conditions. Relying on the resulting quadratic growth condition of th...

Optimality conditions and POD a-posteriori error estimates for a semilinear parabolic optimal control

In the present paper the authors consider an optimal control problem for a parametrized nonlinear parabolic differential equation, which is motivated by lithium-ion battery models. A standard finite element (FE) discretization leads to a large-scale nonlinear optimization problem so that its numerical solution is very costly. Therefore, a reduced-order modelling based on proper orthogonal decom...

A priori error estimates for space-time finite element discretization of semilinear parabolic optimal control problems

In this paper, a priori error estimates for space-time finite element discretizations of optimal control problems governed by semilinear parabolic PDEs and subject to pointwise control constraints are derived. We extend the approach from [23, 24], where linear-quadratic problems have been considered, discretizing the state equation by usual conforming finite elements in space and a discontinuou...

Error Estimates for a Semilinear Elliptic