Abstract
This communication deals with a comparison between two methods of discretization: the well known finite element method and the natural element method that is a meshless method. An error estimator, based on the nonverification of the constitutive law, is used. This estimation has been applied to two examples: a device with permanent magnets and a variable reluctance machine.
Highlights
NOWADAYS, the finite element method (FEM) is well established and allows solving many problems in applied physics
The natural element method [1] belongs to this new and vast family of meshless methods and its interest compared with the vast majority of meshless techniques concern its interpolation property that allows enforcing essential boundary conditions in an easy way, as in the finite element method
We recall that the imposition of essential boundary conditions is the main issue in the other meshless methods
Summary
NOWADAYS, the finite element method (FEM) is well established and allows solving many problems in applied physics. The most usual mesh constraints are related to the need of efficient remeshing procedures, which in the 3-D case constitutes a difficulty nowadays under active investigation, as well as to the field projection from the old mesh to the new mesh that induces an inevitable numerical diffusion whose unfavorable impact on the solution after numerous resmeshing steps is widely accepted. It was in this context that the so-called “meshless methods” were introduced one decade ago.
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