In this paper are analyzed finite element methods based on Powell-Sabin splines, for the solution of partial differential equations in two dimensions. PS splines are piecewise quadratic polynomials defined on a triangulation of the domain, and exhibit a global C 1 continuity. Critical issues when dealing with PS splines, and described in this work, are the construction of the shape functions and the imposition of the boundary conditions. The PS finite element method is used at first to solve an elliptic problem describing plasma equilibrium in a tokamak. Finally, a transient convective problem is also considered, and a stabilized formulation is presented.