Iterative algorithms for higher order finite element schemes

An iterative method for the solution of partial differential equation by higher order finite element method (FEM) on unstructured grids is presented. The algorithms corresponding to lagrangean and hierarchical FEM bases are designed and studied. The results of numerical experiments for a set of the problems (diffusion, convection-diffusion, Euler, Navier–Stokes) are given to show capability of the algorithms.