We rely on a combination of different finite element methods on composite meshes, for the simulation of axisymmetric plasma equilibria in tokamaks. One mesh with Cartesian quadrilaterals covers the vacuum chamber and one mesh with triangles discretizes the region outside the chamber. The two meshes overlap in a narrow region around the chamber. This approach gives the flexibility to achieve easily and at low cost higher order regularity for the approximation of the flux function in the area that is covered by the plasma, while preserving accurate meshing of the geometric details in the exterior. The continuity of the numerical solution across the boundary of each subdomain is enforced by a new mortar-like projection.