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Article
Consistency, stability, a priori and a posteriori errors for Petrov-Galerkin methods applied to nonlinear problems
In an abstract framework we present a formalism which specifies the notions of consistency and stability of Petrov-Galerkin methods used to approximate nonlinear problems which are, in many practical situation...
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Article
Adaptive finite element for semi-linear convection–diffusion problems
In this article a strategy of adaptive finite element for semi-linear problems, based on minimizing a residual-type estimator, is reported. We get an a posteriori error estimate which is asymptotically exact w...
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Article
Identification of the diffusion coefficient for a semi-linear hyperbolic-parabolic problem with discontinuous nonlinear terms
Numerical computations concerning geochemical processes in porous media require a knowledge of the values of the macroscopic parameters. In the context of the interpretation of leaching tests one such paramete...
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Article
A posteriori error estimates and domain decomposition with nonmatching grids
Let F be a nonlinear map** defined from a Hilbert space X into its dual X′, and let x be in X the solution of F(x)=0. Assume that, a priori, the zone where the gradient of the function x has a large variation ...
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Chapter and Conference Paper
Injection Vapour Model in a Porous Medium Accounting for a Weak Condensation
For studying the impact of a hight pressure vapor on a concrete wall, we propose a stationary 3D homogenized model. We show that the interface evolves as a (shock or rarefaction) wave accordingly with the mobi...
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Chapter and Conference Paper
Viscous Drops Spreading With Evaporation And Applications To DNA Biochips
We develop a lubrication model for the viscous drop spreading with evaporation. It is then solved in the quasi-static case and the numerical method is used in the parameter identification in the application to...
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Article
A numerical schema for the transport of nutrients and hormones in plant growth
Classical numerical methods exhibit numerical discrepancies, when we are dealing with the transport equation in domain of heterogeneous sizes. In this work, a numerical scheme, based on a domain decomposition ...