  We consider singularly perturbed boundary value problems with a simple
interior turning point whose solutions exhibit an interior layer. These
problems are discretised using higher order finite elements on layer-adapted
graded meshes proposed by Liseikin. We prove $\epsilon$-uniform error estimates
in the energy norm. Furthermore, for linear elements we are able to prove
optimal order $\epsilon$-uniform convergence in the $L^2$-norm on these graded
meshes.
