44 research outputs found
Block thresholding for wavelet-based estimation of function derivatives from a heteroscedastic multichannel convolution model
We observe heteroscedastic stochastic processes , where
for any and , is the convolution
product of an unknown function and a known blurring function
corrupted by Gaussian noise. Under an ordinary smoothness assumption on
, our goal is to estimate the -th derivatives (in weak
sense) of from the observations. We propose an adaptive estimator based on
wavelet block thresholding, namely the "BlockJS estimator". Taking the mean
integrated squared error (MISE), our main theoretical result investigates the
minimax rates over Besov smoothness spaces, and shows that our block estimator
can achieve the optimal minimax rate, or is at least nearly-minimax in the
least favorable situation. We also report a comprehensive suite of numerical
simulations to support our theoretical findings. The practical performance of
our block estimator compares very favorably to existing methods of the
literature on a large set of test functions
Error estimates for Stokes problem with Tresca friction condition
In this work we propose and study a three field mixed formulation for solving
the Stokes problem with Tresca-type non-linear boundary conditions. Two
Lagrange multipliers are used to enforce div(u)=0 constraint and to regularize
the energy functional. The resulting problem is discretised using "P1
bubble/P1-P1" finite elements. Error estimates are derived and several
numerical studies are achieved
Shape optimization for Stokes problem with threshold slip
summary:We study the Stokes problems in a bounded planar domain with a friction type boundary condition that switches between a slip and no-slip stage. Our main goal is to determine under which conditions concerning the smoothness of solutions to the Stokes system with the slip boundary conditions depend continuously on variations of . Having this result at our disposal, we easily prove the existence of a solution to optimal shape design problems for a large class of cost functionals. In order to release the impermeability condition, whose numerical treatment could be troublesome, we use a penalty approach. We introduce a family of shape optimization problems with the penalized state relations. Finally we establish convergence properties between solutions to the original and modified shape optimization problems when the penalty parameter tends to zero
Méthode d'éléments finis avec hybridisation frontière pour les problèmes de contact avec frottement
National audienc
Algorithme de Neumann–Dirichlet pour des problèmes de contact unilatéral : Résultat de convergence
National audienc
Mixed finite element approximation of 3D contact problems with given friction: Error analysis and numerical realization
This contribution deals with a mixed variational formulation of 3D contact problems with the simplest model involving friction. This formulation is based on a dualization of the set of admissible displacements and the regularization of the non-differentiable term. Displacements are approximated by piecewise linear elements while the respective dual variables by piecewise constant functions on a dual partition of the contact zone. The rate of convergence is established provided that the solution is smooth enough. The numerical realization of such problems will be discussed and results of a model example will be shown
Problème de contact avec frottement (analyse et convergence par méthodes de sous-domaines)
Nous traiterons, dans ce mémoire de doctorat, de l'application des méthodes de décompositions de domaines à la résolution d'inéquations variationnelles. Plus particulièrement, nous adapterons des méthodes existantes pour le cas linéaire de l'élasticité classique au cas non linéaire de la mécanique du contact avec frottement de Tresca. Une partie sera consacrée à la méthode de Neumann-Neumann, une autre pour la méthode de Robin-Robin. Chaque partie sera découpée en chapitre portant sur l'étude de la convergence des algorithmes sous forme continue et discrète. Aussi, leurs robustesses est illustrées par des tests numériques.We propose three non-overlapping domain decomposition methods to approximate contact problem with Tresca friction between two elastic bodies. Two of them are Neumann-Neumann algorithms, the third is a Lions (Robin) one. We prove their convergence in continuous case and their robustness in discrete case. Some numerical experiments illustrate the robustness of these parallel algorithms.CAEN-BU Sciences et STAPS (141182103) / SudocSudocFranceF