  For the Stokes equation over 2D and 3D domains, explicit a posteriori and a
priori error estimation are novelly developed for the finite element solution.
The difficulty in handling the divergence-free condition of the Stokes equation
is solved by utilizing the extended hypercircle method along with the
Scott-Vogelius finite element scheme. Since all terms in the error estimation
have explicit values, by further applying the interval arithmetic and verified
computing algorithms, the computed results provide rigorous estimation for the
approximation error. As an application of the proposed error estimation, the
eigenvalue problem of the Stokes operator is considered and rigorous bounds for
the eigenvalues are obtained. The efficiency of proposed error estimation is
demonstrated by solving the Stokes equation on both convex and non-convex 3D
domains.
