In this article, global stabilization results for the two dimensional 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.

在本文中，使用非线性诺伊曼边界反馈控制律，建立了二维粘性Burgers方程的整体稳定结果，即，非稳态解与任何初始数据的恒定稳态解的收敛。然后，在空间方向上应用\（C ^ 0 \）协调有限元方法，在\（L ^ \ infty（L ^ 2）\）和\（L ^ \ infty（H ^ 1）\ ）-得出状态变量的范数和边界反馈控制律的收敛结果。所有结果都保留了指数稳定特性。最后，进行了一些数值实验以证实我们的理论发现。