The Hierarchical Basis Extrapolation Method

Traditional extrapolation methods, like Richardson’s extrapolation, are based on asymptotic error expansions of the solution, and thus depend on the use of uniform grids. Within the hierarchical basis framework for the finite element method it is natural to consider an extrapolation of the energy functional. This idea is based on a purely local element-by-element analysis and is applicable to irregular and unstructured meshes. It will be demonstrated that higher order discretization can be obtained by this type of extrapolation without imposing any additional restrictions on the finite element mesh. This method is especially well suited for use in combination with local refinement strategies. If combined with a multilevel solution procedure, the algorithm is closely related to multigrid tau-extrapolation. This paper will present the theoretical background and experimental results for the energy extrapolation method in hierarchical basis formulation.