  This work develops an epsilon-uniform finite element method for singularly
perturbed boundary value problems. A surprising and remarkable observation is
illustrated: By moving one node arbitrarily in between its adjacent nodes, the
new finite element solution always intersect with original one at fixed point.
Using this fact, an effective epsilon-uniform approximation out of boundary is
proposed by adding one point only in the grid that contains boundary layer. The
thickness of boundary layer is not necessary to be known from priori
estimation. Numerical results are carried out and compared to Shishkin mesh for
demonstration purpose.
