Continuous enrichment for advection-dominated problems
Résumé
We are interested in advection-diffusion problems with high Peclet number when shock like structure in the domain and strong boundary-layers both exist. This boundary-layer, though very thin, concentrates most degrees of freedom to get acceptable accuracy. We aim at designing a numerical framework able to reduce dramaticaly their number in the boundary-layer. This is done via a stabilized enriched finite elements method with Lagrange multipliers to enforce boundary conditions.