When on/off switches are triggered at discrete time levels by a threshold condition in a traditionally discretized model, the model solution is not continuously dependent on the initial state and this causes problems in tangent linearization and adjoint computations. It is shown in this paper that the problems can be avoided by introducing coarse-grain tangent linearization and adjoint without ...

This work proposes a new adaptive remeshing strategy based on the sensitivity of the point wise error in stresses with respect to the nodal coordinates, which is computed using the adjoint-state method. This sensitivity provides information about the influence of the discretization of each zone of the computational domain in the estimation of the error in stresses at a specific point. This info...

An optimal control problem for a 2-d elliptic equation is investigated with pointwise control constraints. This paper is concerned with discretization of the control by piecewise linear functions. The state and the adjoint state are discretized by linear finite elements. Approximation of order h in the L-norm is proved in the main result.

An optimal control problem for 2d and 3d Stokes equations is investigated with pointwise control constraints. This paper is concerned with the discretization of the control by piecewise constant functions. The state and the adjoint state are discretized by finite element schemes. In the paper a postprocessing strategy is suggested, which allows for significant improvement of the accuracy.

We analyze a finite element approximation of an elliptic optimal control problem with pointwise bounds on the gradient of the state variable. We derive convergence rates if the control space is discretized implicitly by the state equation. In contrast to prior work we obtain these results directly from classical results for the W 1,∞-error of the finite element projection, without using adjoint...

We analyze a finite element approximation of an elliptic optimal control problem with pointwise bounds on the gradient of the state variable. We derive convergence rates if the control space is discretized implicitly by the state equation. In contrast to prior work we obtain these results directly from classical results for the W 1,∞-error of the finite element projection, without using adjoint...

a mathematical model is presented in the present study to control‎ ‎the light propagation in an inhomogeneous media‎. ‎the method is ‎based on the identification of the optimal materials distribution‎ ‎in the media such that the trajectories of light rays follow the‎ ‎desired path‎. ‎the problem is formulated as a distributed parameter ‎identification problem and it is solved by a numerical met...

The focus of CFD applications has shifted to aerodynamic design. This shift has been mainly motivated by the availability of high performance computing platforms and by the development of new and efficient analysis and design algorithms. In particular automatic design procedures, which use CFD combined with gradient-based optimization techniques, have had a significant impact on the design proc...

In aerodynamics, Optimal Shape Design (OSD) aims to find the minimum of an objective function describing an aerodynamic property, by controlling the Partial Differential Equation (PDE) modeling the dynamics of the flow that surrounds an aircraft. The objective function minimization is usually achieved by means of an iterative process which requires the computation of the gradients of the cost f...

The multi-dimensional Black-Scholes equation is solved numerically for a European call basket option using a priori–a posteriori error estimates. The equation is discretized by a finite difference method on a Cartesian grid. The grid is adjusted dynamically in space and time to satisfy a bound on the global error at the expiry date. The discretization errors in each time step are estimated and ...