A Theoretical Framework for Generalized Hierarchical Approaches Referred to Local Mesh Refinement

This paper proposes a theoretical framework in which generalized hierarchical approaches for the adaptive finite element mesh refinement can be easily designed. Such a generalized approach aims at coupling the classical h version hierarchical adaptive finite element method and the adaptive remeshing strategy. On one hand, the hierarchical aspect should provide such an approach with its iterative multi-mesh solvers and a multi-layer representation of numerical results, which constitutes an appropriate formalism to introduce multi-scale or multi-model analyses. On the other hand the remeshing technique should provide a great flexibility in the generation of new meshes, which becomes necessary when, for example, anisotropic mesh adaptation should be somewhere envisaged.