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In this article, global stabilization results for theBenjamin-Bona-Mahony-Burgers' (BBM-B) type equations are obtained usingnonlinear Neumann boundary feedback control laws. Based on the $C^0$-conformingfinite element method, global stabilization results for the semidiscretesolution are also discussed. Optimal error estimates in $L^\infty(L^2)$,$L^\infty(H^1)$ and $L^\infty(L^\infty)$-norms for the state variable arederived, which preserve exponential stabilization property. Moreover, for thefirst time in the literature, superconvergence results for the boundaryfeedback control laws are established. Finally, several numerical experimentsare conducted to confirm our theoretical findings.

Global Stabilization of BBM-Burgers' Type Equations by Nonlinear Boundary Feedback Control Laws: Theory and Finite Element Error Analysis