On the convergence of some methods for variational inclusions
On the Convergence of the Approximate Free Boundary for the Parabolic Obstacle Problem
Si discretizza il problema dell'ostacolo parabolico con differenze all'indietro nel tempo ed elementi finiti lineari nello spazio e si dimostrano stime dell'errore per la frontiera libera discreta.
On the convergence rate of approximation schemes for Hamilton-Jacobi-Bellman equations
Using systematically a tricky idea of N.V. Krylov, we obtain general results on the rate of convergence of a certain class of monotone approximation schemes for stationary Hamilton-Jacobi-Bellman equations with variable coefficients. This result applies in particular to control schemes based on the dynamic programming principle and to finite difference schemes despite, here, we are not able to treat the most general case. General results have been obtained earlier by Krylov for finite difference...
On the convergence rate of approximation schemes for Hamilton-Jacobi-Bellman Equations
Using systematically a tricky idea of N.V. Krylov, we obtain general results on the rate of convergence of a certain class of monotone approximation schemes for stationary Hamilton-Jacobi-Bellman equations with variable coefficients. This result applies in particular to control schemes based on the dynamic programming principle and to finite difference schemes despite, here, we are not able to treat the most general case. General results have been obtained earlier by Krylov for finite...
On the Efficient Solution of Nonlinear Finite Element Equations. II. Bound-Constrained Problems.
On the Efficient Solution of Nonlinear Finite Element Equations I.
On the generalized Riccati matrix differential equation. Exact, approximate solutions and error estimate
In this paper explicit expressions for solutions of Cauchy problems and two-point boundary value problems concerned with the generalized Riccati matrix differential equation are given. These explicit expressions are computable in terms of the data and solutions of certain algebraic Riccati equations related to the problem. The interplay between the algebraic and the differential problems is used in order to obtain approximate solutions of the differential problem in terms of those of the algebraic...
On the minimization of some nonconvex double obstacle problems.
On the nonlinear implicit complementarity problem.
On the notion of Jacobi fields in constrained calculus of variations
In variational calculus, the minimality of a given functional under arbitrary deformations with fixed end-points is established through an analysis of the so called second variation. In this paper, the argument is examined in the context of constrained variational calculus, assuming piecewise differentiable extremals, commonly referred to as extremaloids. The approach relies on the existence of a fully covariant representation of the second variation of the action functional, based on a family of...
On the Numerical Analysis of the Von Karman Equations : Mixed Finite Element Approximation and Continuation Techniques.
On the numerical solution of axisymmetric domain optimization problems
An axisymmetric second order elliptic problem with mixed boundarz conditions is considered. A part of the boundary has to be found so as to minimize one of four types of cost functionals. The numerical realization is presented in detail. The convergence of piecewise linear approximations is proved. Several numerical examples are given.
On the optimal setting of the -version of the finite element method
The goal of this contribution is to find the optimal finite element space for solving a particular boundary value problem in one spatial dimension. In other words, the optimal use of available degrees of freedom is sought after. This is done through optimizing both the mesh and the polynomial degree of the basis functions. The resulting combinatorial optimization problem is solved in parallel by a Matlab program running on a cluster of multi-core personal computers.
On the optimization of non periodic homogenized microstructures
On the parameter selection problem in the Newton-ADI iteration for large-scale Riccati equations.
On the representation of trajectories of bilinear systems and its applications
On the set of weighted least squares solutions of systems of convex inequalities
Open problems in nonlinear conjugate gradient algorithms for unconstrained optimization.
Optimal control and numerical adaptivity for advection–diffusion equations
We propose a general approach for the numerical approximation of optimal control problems governed by a linear advection–diffusion equation, based on a stabilization method applied to the lagrangian functional, rather than stabilizing the state and adjoint equations separately. This approach yields a coherently stabilized control problem. Besides, it allows a straightforward a posteriori error estimate in which estimates of higher order terms are needless. Our a posteriori estimates stems from splitting...
Optimal control and numerical adaptivity for advection–diffusion equations
We propose a general approach for the numerical approximation of optimal control problems governed by a linear advection–diffusion equation, based on a stabilization method applied to the Lagrangian functional, rather than stabilizing the state and adjoint equations separately. This approach yields a coherently stabilized control problem. Besides, it allows a straightforward a posteriori error estimate in which estimates of higher order terms are needless. Our a posteriori estimates stems from...