A new coordinate transform for the finite element solution of axisymmetric problems in magnetostatics. Melissen, J. & Simkin, J. IEEE Transactions on Magnetics, 26(2):391–394, IEEE, March, 1990.
doi  abstract   bibtex   
It is pointed out that, although field computation in two-dimensional (2-D) axial symmetric problems has a longstanding history and its software has acquired the status of robustness and reliability, problems with singularities in the neighborhood of r =0 still remain a point of concern. A simple example is shown which exhibits a disturbing lack of accuracy and seems to mock all ideas of reasonability of finite-element solutions. A simple solution to the problem is presented, consisting of transforming the vector potential into a form which is better adapted to the bilinear interpolation used in first-order finite elements. For one-dimensional problems with piecewise linear materials this approach yields exact solutions; an increase in accuracy was obtained for other problems also
@Article{         Melissen_1990aa,
  abstract      = {It is pointed out that, although field computation in two-dimensional (2-D) axial symmetric problems has a longstanding history and its software has acquired the status of robustness and reliability, problems with singularities in the neighborhood of r =0 still remain a point of concern. A simple example is shown which exhibits a disturbing lack of accuracy and seems to mock all ideas of reasonability of finite-element solutions. A simple solution to the problem is presented, consisting of transforming the vector potential into a form which is better adapted to the bilinear interpolation used in first-order finite elements. For one-dimensional problems with piecewise linear materials this approach yields exact solutions; an increase in accuracy was obtained for other problems also},
  author        = {Melissen, J.B.M. and Simkin, J.},
  doi           = {10.1109/20.106336},
  file          = {Melissen_1990aa.pdf},
  issn          = {0018-9464},
  journal       = {IEEE Transactions on Magnetics},
  keywords      = {axisymmetric,fem,2d,magnetics,magnetostatics},
  langid        = {english},
  month         = mar,
  number        = {2},
  pages         = {391--394},
  publisher     = {IEEE},
  title         = {A new coordinate transform for the finite element solution of axisymmetric problems in magnetostatics},
  volume        = {26},
  year          = {1990},
  shortjournal  = {IEEE Trans. Magn.}
}
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