505 research outputs found
A Mixed Method for Axisymmetric Div-Curl Systems
We present a mixed method for a three-dimensional axisymmetric div-curl system reduced to a two-dimensional computational domain via cylindrical coordinates. We show that when the meridian axisymmetric Maxwell problem is approximated by a mixed method using the lowest order Nédélec elements (for the vector variable) and linear elements (for the Lagrange multiplier), one obtains optimal error estimates in certain weighted Sobolev norms. The main ingredient of the analysis is a sequence of projectors in the weighted norms satisfying some commutativity properties
3D direct and inverse solvers for eddy current testing of deposits in steam generator
We consider the inverse problem of estimating the shape profile of an unknown
deposit from a set of eddy current impedance measurements. The measurements are
acquired with an axial probe, which is modeled by a set of coils that generate
a magnetic field inside the tube. For the direct problem, we validate the
method that takes into account the tube support plates, highly conductive part,
by a surface impedance condition. For the inverse problem, finite element and
shape sensitivity analysis related to the eddy current problem are provided in
order to determine the explicit formula of the gradient of a least square
misfit functional. A geometrical-parametric shape inversion algorithm based on
cylindrical coordinates is designed to improve the robustness and the quality
of the reconstruction. Several numerical results are given in the experimental
part. Numerical experiments on synthetic deposits, nearby or far away from the
tube, with different shapes are considered in the axisymmetric configuration.Comment: 3
On the global well-posedness for the Boussinesq system with horizontal dissipation
In this paper, we investigate the Cauchy problem for the tridimensional
Boussinesq equations with horizontal dissipation. Under the assumption that the
initial data is an axisymmetric without swirl, we prove the global
well-posedness for this system. In the absence of vertical dissipation, there
is no smoothing effect on the vertical derivatives. To make up this
shortcoming, we first establish a magic relationship between
and by taking full advantage of the structure of the
axisymmetric fluid without swirl and some tricks in harmonic analysis. This
together with the structure of the coupling of \eqref{eq1.1} entails the
desired regularity.Comment: 32page
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