It is shown that the solution of a rotating plasma problem minimizes a quitably chosen funtional. This variational problem is solved by the Ritz-Galerkin methud using piecewise bilinear functions and applying some Newton-Côtes-like quadrature. The resulting linear system with a sparse nonegative definite matrix is dolved by an adapted conjugate gradient method.
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Computer Physics Communications
Multiscale Dynamics

Bakker, M, & van den Berg, M.S. (1980). A program to solve rotating plasma problems. Computer Physics Communications, 20(3), 429–439.