ﻻ يوجد ملخص باللغة العربية
In this article, global stabilization results for the Benjamin-Bona-Mahony-Burgers (BBM-B) type equations are obtained using nonlinear Neumann boundary feedback control laws. Based on the $C^0$-conforming finite element method, global stabilization results for the semidiscrete solution 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 are derived, which preserve exponential stabilization property. Moreover, for the first time in the literature, superconvergence results for the boundary feedback control laws are established. Finally, several numerical experiments are conducted to confirm our theoretical findings.
In this article, global stabilization results for the two dimensional (2D) 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 boun
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
We study the problem of global exponential stabilization of original Burgers equations and the Burgers equation with nonlocal nonlinearities by controllers depending on finitely many parameters. It is shown that solutions of the controlled equations
The paper is concerned with the adaptive finite element solution of linear elliptic differential equations using equidistributing meshes. A strategy is developed for defining this type of mesh based on residual-based a posteriori error estimates and
We discuss the error analysis of the lowest degree Crouzeix-Raviart and Raviart-Thomas finite element methods applied to a two-dimensional Poisson equation. To obtain error estimations, we use the techniques developed by Babuv{s}ka-Aziz and the autho