An iteration method for high order finite element schemes. Part I

An approach to development of iterative algorithms for the solution of hp-discretization on unstructured grids is presented. This approach is applied for solution of PDEs (Poisson, anisotropic diffusion, convection-diffusion) discretized by finite element method (FEM) or stabilized FEM. Two variants of the algorithm corresponding to lagrangean and hierarchical FEM bases are designed and studied. The results of numerical experiments are presented to show capability of the algorithm.