  In this article, global stabilization results for the two dimensional (2D)
viscous Burgers' equation, that is, convergence of unsteady solution to its
constant steady state solution with any initial data, are established using a
nonlinear Neumann boundary feedback control law. Then, applying
$C^0$-conforming finite element method in spatial direction, optimal error
estimates in $L^\infty(L^2)$ and in $L^\infty(H^1)$- norms for the state
variable and convergence result for the boundary feedback control law are
derived. All the results preserve exponential stabilization property. Finally,
several numerical experiments are conducted to confirm our theoretical
findings.
