Convergence of a Penalty-Finite Element Approximation for an Obstacle Problem.
Convergence of approximate solutions of variational problems
Convergence of Cell Based Finite Volume Discretizations for Problems of Control in the Conduction Coefficients
We present a convergence analysis of a cell-based finite volume (FV) discretization scheme applied to a problem of control in the coefficients of a generalized Laplace equation modelling, for example, a steady state heat conduction. Such problems arise in applications dealing with geometric optimal design, in particular shape and topology optimization, and are most often solved numerically utilizing a finite element approach. Within the FV framework for control in the coefficients problems ...
Convergence of Cell Based Finite Volume Discretizations for Problems of Control in the Conduction Coefficients
We present a convergence analysis of a cell-based finite volume (FV) discretization scheme applied to a problem of control in the coefficients of a generalized Laplace equation modelling, for example, a steady state heat conduction. Such problems arise in applications dealing with geometric optimal design, in particular shape and topology optimization, and are most often solved numerically utilizing a finite element approach. Within the FV framework for control in the coefficients problems ...
Convergence of convex functions and generalized inf-convolutive approximations. (Convergences des fonctions convexes et approximations inf-convolutives généralisées.)
Convergence of convex-concave saddle functions : applications to convex programming and mechanics
Convergence of discontinuous Galerkin approximations of an optimal control problem associated to semilinear parabolic PDE's
A discontinuous Galerkin finite element method for an optimal control problem related to semilinear parabolic PDE's is examined. The schemes under consideration are discontinuous in time but conforming in space. Convergence of discrete schemes of arbitrary order is proven. In addition, the convergence of discontinuous Galerkin approximations of the associated optimality system to the solutions of the continuous optimality system is shown. The proof is based on stability estimates at arbitrary time...
Convergence of iterative sequences for generalized equilibrium problems involving inverse-strongly monotone mappings.
Convergence of numerical methods and parameter dependence of min-plus eigenvalue problems, Frenkel-Kontorova models and homogenization of Hamilton-Jacobi equations
Using the min-plus version of the spectral radius formula, one proves: 1) that the unique eigenvalue of a min-plus eigenvalue problem depends continuously on parameters involved in the kernel defining the problem; 2) that the numerical method introduced by Chou and Griffiths to compute this eigenvalue converges. A toolbox recently developed at I.n.r.i.a. helps to illustrate these results. Frenkel-Kontorova models serve as example. The analogy with homogenization of Hamilton-Jacobi equations is emphasized....
Convergence of numerical methods and parameter dependence of min-plus eigenvalue problems, Frenkel-Kontorova models and homogenization of Hamilton-Jacobi equations
Using the min-plus version of the spectral radius formula, one proves: 1) that the unique eigenvalue of a min-plus eigenvalue problem depends continuously on parameters involved in the kernel defining the problem; 2) that the numerical method introduced by Chou and Griffiths to compute this eigenvalue converges. A toolbox recently developed at I.n.r.i.a. helps to illustrate these results. Frenkel-Kontorova models serve as example. The analogy with homogenization of Hamilton-Jacobi equations...
Convergence of optimal solutions in control problems for hyperbolic equations
A sequence of optimal control problems for systems governed by linear hyperbolic equations with the nonhomogeneous Neumann boundary conditions is considered. The integral cost functionals and the differential operators in the equations depend on the parameter k. We deal with the limit behaviour, as k → ∞, of the sequence of optimal solutions using the notions of G- and Γ-convergences. The conditions under which this sequence converges to an optimal solution for the limit problem are given.
Convergence of the coincidence set in the homogenization of the obstacle problem
Convergence of the time-discretized monotonic schemes
Many numerical simulations in (bilinear) quantum control use the monotonically convergent Krotov algorithms (introduced by Tannor et al. [Time Dependent Quantum Molecular Dynamics (1992) 347–360]), Zhu and Rabitz [J. Chem. Phys. (1998) 385–391] or their unified form described in Maday and Turinici [J. Chem. Phys. (2003) 8191–8196]. In Maday et al. [Num. Math. (2006) 323–338], a time discretization which preserves the property of monotonicity has been presented. This paper introduces a proof of...
Convergence of unilateral convex sets in higher order Sobolev spaces
Convergence rate of the solutions of singularly perturbed time-optimal control problems
Convergence theorem based on a new hybrid projection method for finding a common solution of generalized equilibrium and variational inequality problems in Banach spaces.
Convergence theorems for generalized projections and maximal monotone operators in Banach spaces.
Convergence theorems on generalized equilibrium problems and fixed point problems with applications.
Convergence uniforme pour les itérés définissant la solution d'une inéquation quasi-variationnelle
Convergences et relations compactantes. Application aux équilibres de Stackelberg