A Finite Element Method for the Boundary Data Recovery in an Oxygen-Balance Dispersion Model

International audienceThe inverse problem under investigation consists of the boundary data completion in a deoxygenation-reaeration model in stream-waters. The unidimensional transport model we deal with is based on the one introduced by Streeter and Phelps, augmented by Taylor dispersion terms. The missing boundary condition is the load or/and the flux of the biochemical oxygen demand indicator at the outfall point. The counterpart is the availability of two boundary conditions on the dissolved oxygen tracer at the same point. The major consequences of these non-standard boundary conditions is that dispersive transport equations on both oxygen tracers are strongly coupled and the resulting system becomes ill-posed. The main purpose is a finite element space-discretization of the variational problem put under a non-symmetric mixed form. Combining analytical calculations, numerical computations and theoretical justifications, we try to elucidate the characteristics related to the ill-posedness of this data completion dynamical problem and understand its mathematical structure

Méthode des éléments finis max-plus pour la résolution numérique de problèmes de commande optimale déterministe

PARIS-BIUSJ-Thèses (751052125) / SudocPARIS-BIUSJ-Physique recherche (751052113) / SudocSudocFranceF

Singular perturbation for the Dirichlet boundary control of elliptic problems

A current procedure that takes into account the Dirichlet boundary condition with non-smooth data is to change it into a Robin type condition by introducing a penalization term; a major effect of this procedure is an easy implementation of the boundary condition. In this work, we deal with an optimal control problem where the control variable is the Dirichlet data. We describe the Robin penalization, and we bound the gap between the penalized and the non-penalized boundary controls for the small penalization parameter. Some numerical results are reported on to highlight the reliability of such an approach

Numerical Simulation of the Wave Equation with Discontinuous Coefficients by Nonconforming Finite Elements

International audienceThe goal of this article is to apply the mortar finite element method to the numerical simulation of (elec- tromagnetic and/or acoustic) waves propagating in an inhomogeneous support. This approach allows us to use meshes well adapted to the local physical parameters of the media without any conformity constraints. A complete mathematical study is supplied providing the expected optimal convergence rate. Numerical performances of such a technique, as well as its advantages, are also discussed

Spectral and High Order Methods for Partial Differential Equations - ICOSAHOM 2012Selected papers from the ICOSAHOM conference, June 25-29, 2012, Gammarth, Tunisia /

IX, 425 p. 145 illus., 71 illus. in color.online