Abstract
AbstractIn 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 $$C^0$$
C
0
-conforming finite element method in spatial direction, optimal error estimates in $$L^\infty (L^2)$$
L
∞
(
L
2
)
and in $$L^\infty (H^1)$$
L
∞
(
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.
Publisher
Springer Science and Business Media LLC
Subject
Computational Theory and Mathematics,General Engineering,Theoretical Computer Science,Software,Applied Mathematics,Computational Mathematics,Numerical Analysis
Cited by
3 articles.
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