Numerically stable finite element methods for the Galerkin solution of eddy current problems

Two sources of error that contribute to the instability of Galerkin solutions of vector eddy-current problems are identified. The first results from a magnification of the error in modeling or integrating the solenoidal forcing function. The second arises from contamination of the deterministic solutions by spurious modes. To obtain stable finite-element solutions of vector eddy-current problems, it is therefore necessary to model the forcing function accurately and to use vector basis functions that do not produce spurious modes. Two such sets of stable basis functions are found to be standard Lagrangian elements on a common C¹ mesh and tangential vector elements on an arbitrary mesh