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

Global Stabilization of Two Dimensional Viscous Burgers' Equation by Nonlinear Neumann Boundary Feedback Control and its Finite Element Analysis