For the discretization of the underlying spherical shallow water equations a Lagrange–Galerkin method is used. The unstructured triangular grid is maintained by the grid generator amatos and the large linear systems are solved by the parallel solver interface FoSSI. Experimental convergence is shown by means of steady-state and unsteady analytical solutions. PLASMA yields satisfactory results for quasi standard experiments, that is the Rossby–Haurwitz wave and zonal flows over an isolated mountain.