AlejandroFN
Subscriber

Hi Paul,

Thank you very much for the answer.

The thing is that we have observed that the local error increases when refining the mesh. There are singularities in inner sharp corners, in which the result does not converge when refining the mesh. We think that this is the same case as the singularities explained in this paper: https://ieeexplore.ieee.org/document/877575 

You said that there is a "weakly-imposed" divergence calculation. This seems equivalent to the case explained in the mentioned paper, where they use the Coulomb gauge (rho*Div T=0) in a weakly-imposed way, leading to non-zero divergence in inner corners of the geometry. Do you agree that this is the cause of our local errors? Do you use this Coulomb gauge as well in your formulation?

I performed several simulations to show how this error increases when refining the mesh: For a 25 mm max. element size in the whole geometry I get a 0.001471% energy error, while this error increases up to 0.001538% when applying local refinements in the regions with high variation of eddy currents.

On the other hand, for a specific corner with high variation of eddy currents I applied further local mesh refinements to study the evolution of the peak electromagnetic force when refining the mesh and its relation with the divergence of B.

The peak volumetric force increases without convergence when refining the local mesh:

The trend is the same of the divergence of B in the same zone. When refining the mesh, the error increases: