Fake Conductivity or Cohomology: Which to Use When Solving Eddy Current Problems With $h$ -Formulations?

There are two ways of solving eddy current problems with an edge element h-conforming formulation in the case of non-simply-connected conductors: first employs a “fake” artificial conductivity in part of the insulator. Second uses the cohomology theory to define a scalar magnetic potential in the whole insulator. This contribution provides, for the first time, a thorough comparison between these methods. We concentrate on the accuracy and computational effort required to solve a problem using both of the two methods.