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We describe in this report the numerical analysis of a particular class of nonlinear Dirichlet problems. We consider an equivalent variational inequality formulation on which the problems of existence, uniqueness and approximation are easier to discuss. We prove in particular the convergence of an approximation by piecewise linear finite elements. Finally,(More)
— In this article, we address the numerical solution of a non-smooth eigenvalue problem, which has implications in plasticity theory and image processing. The smallest eigenvalue of the non-smooth operator under consideration is shown to be the same for all bounded, sufficiently smooth, domains in two space dimensions. Piecewise linear finite elements are(More)
The main goal of this article is to review various results and methods concerning the numerical simulation of Bingham visco-plastic flow; these results have been obtained from the early 1970s to now. We consider first the case of flow in cylindrical pipes and then flow in multi-dimensional cavities. The methods to be discussed include classical ones relying(More)
We introduce a novel loosely coupled-type algorithm for fluid-structure interaction between blood flow and vascular walls. This algorithm successfully deals with the difficulties associated with the " added mass effect " , which is known to be the cause of numerical instabilities in fluid-structure interaction problems involving fluid and structure of(More)
The main goal of this article is to investigate the capability of an operator-splitting/finite elements based methodology at handling accurately incompressible viscous flow at large Reynolds number (Re) in regions with corners and curved boundaries. To achieve this goal the authors have selected a wall-driven flow in a semi-circular cavity. On the basis of(More)