Adaptive mesh refinement in the finite element computation of magnetic fields

Abstract

Adaptive mesh refinement has the potential of making the finite element computation of magnetic field problems completely automatic. In adaptive procedures, the field problem is solved iteratively, beginning with a coarse mesh and refining it in locations of greatest error. Methods of mesh refinement for triangular finite element grids are surveyed and the use of local error estimates in the adaptive process is described. It is concluded that the Delaunay triangulation provides the best method of mesh refinement, while complementary variational principles provide accurate error bounds on the solution.