Composite grid finite element method: Implementation and iterative solution with inexact subproblems

This paper concerns the composite grid finite element (FE) method for solving boundary value problems in the cases which require local grid refinement for enhancing the approximating properties of the corresponding FE space. A special interest is given to iterative methods based on natural decomposition of the space of unknowns and to the implementation of both the composite grid FEM and the iterative procedures for its solution. The implementation is important for gaining all benefits of the described methods. We also discuss the case of inexact subproblems, which can frequently arise in the course of hierarchical modelling.