Section: New Results

Boundary Layer Enrichment

Participants : Rémi Abgrall [Corresponding member] , Arnaud Krust.

Arnaud Krust has finished his PhD thesis on boundary layer enrichment. We developed a numerical framework well suited for advection- diffusion problems when the advection part is dominant. In that case, given Dirichlet type boundary condition, it is well known that a boundary layer develops. In order to resolve correctly this layer, standard methods consist in increasing the mesh resolution and possibly increasing the formal accuracy of the numerical method. In this work, we follow another path: we do not seek to increase the formal accuracy of the scheme but, by a careful choice of finite element, to lower the mesh resolution in the layer. Indeed the finite element representation we choose is locally the sum of a standard one plus an enrichment. This work proposes such a method and with several numerical examples, we show the potential of this approach. In particular we show that the method is not very sensitive to the choice of the enrichment functions. The best choice of enrichment are shown to be obtained by an iterative mechanisms which bears some common features with mesh refinement.