  Global stabilization of viscous Burgers' equation around constant steady
state solution has been discussed in the literature. The main objective of this
paper is to show global stabilization results for the 2D forced viscous
Burgers' equation around a nonconstant steady state solution using nonlinear
Neumann boundary feedback control law, under some smallness condition on that
steady state solution. On discretizing in space using $C^0$ piecewise linear
elements keeping time variable continuous, a semidiscrete scheme is obtained.
Moreover, global stabilization results for the semidiscrete solution and
optimal error estimates for the state variable in $L^\infty(L^2)$ and
$L^\infty(H^1)$-norms are derived. Further, optimal convergence result is
established for the boundary feedback control law. All our results in this
paper preserve exponential stabilization property. Finally, some numerical
experiments are documented to confirm our theoretical findings.

Optimization and Control;Numerical Analysis;Numerical Analysis