Quasioptimal uniformly convergent finite element methods for the elliptic boundary layer problem (Q1368480)

The author deals with the numerical solution of a model two-dimensional second-order elliptic boundary value problem with a small parameter at the higher derivative with respect to one of the variables. The solution of this problem has boundary layers and classical finite difference methods often produce numerical pathologies. The bilinear finite element method on a special nonuniform grid is proposed and investigated. Using the boundary layer correction technique and elaborating barrier functions the method is shown to be convergent uniformly in the perturbation parameter. The results are illustrated by numerical examples.