We wish to show how the shock position in a nozzle could be controlled. Optimal control theory and algorithm is applied to the transonic equation. The difficulty is that the derivative with respect to the shock position involves a Dirac mass. The one dimensional case is solved, the two dimensional one is analyzed .
This paper deals with a nonlinear beam model which was published by D. Y. Gao in 1996. It is considered either pure bending or a unilateral contact with elastic foundation, where the normal compliance condition is employed. Under additional assumptions on data, higher regularity of solution is proved. It enables us to transform the problem into a control variational problem. For basic types of boundary conditions, suitable transformations of the problem are derived. The control variational problem...
A new algorithm which generalizes the E-algorithm is presented. It is called the -algorithm. Some results on convergence acceleration for the -algorithm are proved. Some applications are given.
The paper is devoted to the convergence analysis of a well-known cell-centered Finite Volume Method (FVM) for a convection-diffusion problem in . This FVM is based on Voronoi boxes and exponential fitting. To prove the convergence of the FVM, we use a new nonconforming Petrov-Galerkin Finite Element Method (FEM) for which the system of linear equations coincides completely with that of the FVM. Thus, by proving convergence properties of the FEM we obtain similar ones for the FVM. For the error...
We present and analyse in this paper a novel cell-centered collocated finite volume scheme for incompressible flows. Its definition involves a partition of the set of control volumes; each element of this partition is called a cluster and consists in a few neighbouring control volumes. Under a simple geometrical assumption for the clusters, we obtain that the pair of discrete spaces associating the classical cell-centered approximation for the velocities and cluster-wide constant pressures is inf-sup...
In this paper, we propose a new class of adaptive trust region methods for unconstrained optimization problems and develop some convergence properties. In the new algorithms, we use the current iterative information to define a suitable initial trust region radius at each iteration. The initial trust region radius is more reasonable in the sense that the trust region model and the objective function are more consistent at the current iterate. The global convergence, super-linear and quadratic convergence...