On quasi-reversibility solutions to the Cauchy problem for the Laplace equation: regularity and error estimates

We are interested in the classical ill-posed Cauchy problem for the Laplace equation. One method to approximate the solution associated with compatible data consists in considering a family of regularized well-posed problems depending on a small parameter ε > 0. In this context, in order to prove convergence of finite elements methods, it is necessary to get regularity results of the solutions to these regularized problems which hold uniformly in ε. In the present work, we obtain these results in smooth domains and in 2D polygonal geometries. In presence of corners, due to the particular structure of the regularized problems, classical techniques à la Grisvard do not work and instead, we apply the Kondratiev approach. We describe the procedure in detail to keep track of the dependence in ε in all the estimates. The main originality of this study lies in the fact that the limit problem is ill-posed in any framework.

A semi-analytical method to compute the magnetic flux linkage of a 2D meshed coil in presence of magnetic materials − application to electrical motor pre-design

This paper provides a semi-analytical approach for computing the flux linkage of a 2D meshed coil in presence of a non-linear magnetic material. First, a method for flux computation is introduced given the field obtained thanks to a volume integral method. Second, an analytical method for computing the magnetic source field and magnetic vector potential induced by a 2D meshed coil is presented, those quantities being necessary for the flux computation. Comparisons to the finite elements methods are carried out to conclude on the performances of the new method presented.

The Design and Simulation Analysis of Halbach Permanent Maglev Positioning Platform

The thesis put forward a new maglev positioning platform whose structure, theories of operation and modeling were discussed. Applying finite elements methods in electromagnetic simulation and thermal simulation of the structure, the feasibility of the new platform was proved.