An analysis of finite element locking in a parameter dependent model problem

We consider the bilinear finite element approximation of smooth solutions t o a simple parameter dependent elliptic model problem, the problem of highl y anisotropic heat conduction. We show that under favorable circumstances t hat depend on both the finite element mesh and on the type of boundary cond itions, the effect of parametric locking of the standard FEM can be reduced by a simple variational crime. In our analysis we split the error in two o rthogonal components, the approximation error and the consistency error, an d obtain different bounds for these separate components. Also some numerica l results are shown.