The variational treatment of the diffusion equation for vector field problems

A new and efficient technique for the solution of axisymmetric vector potential problems described by the diffusion equation is reported. The equation is solved using the finite element method, and the corresponding element matrices are derived and extensively tested computationally. The numerical results obtained for a simple structure are compared with the exact analytical solution. A difficult problem originating from the area of nuclear power engineering illustrates the application of the method to practial engineering problems.