  Optimally convergent (with respect to the regularity) quadratic finite
element method for two dimensional obstacle problem on simplicial meshes is
studied in (Brezzi, Hager, Raviart, Numer. Math, 28:431--443, 1977). There was
no analogue of a quadratic finite element method on tetrahedron meshes for
three dimensional obstacle problem. In this article, a quadratic finite element
enriched with element-wise bubble functions is proposed for the three
dimensional elliptic obstacle problem. A priori error estimates are derived to
show the optimal convergence of the method with respect to the regularity.
Further a posteriori error estimates are derived to design an adaptive mesh
refinement algorithm. Numerical experiment illustrating the theoretical result
on {\em a priori} error estimate is presented.
