  We verify functional a posteriori error estimate for obstacle problem
proposed by Repin. Simplification into 1D allows for the construction of a
nonlinear benchmark for which an exact solution of the obstacle problem can be
derived. Quality of a numerical approximation obtained by the finite element
method is compared with the exact solution and the error of approximation is
bounded from above by a majorant error estimate. The sharpness of the majorant
error estimate is discussed.
