In this Note, we study the indirect boundary stabilization of the Timoshenko system with only one... more In this Note, we study the indirect boundary stabilization of the Timoshenko system with only one dissipation law. Under the equal speed wave propagation condition, we establish the exponential stability of the system. On the contrary, we show that the decay rate is polynomial.
In this paper we develop an a posteriori error analysis of a nonconforming mixed finite element m... more In this paper we develop an a posteriori error analysis of a nonconforming mixed finite element method for the coupling of fluid flow with porous media flow. The approach utilizes the same nonconforming Crouzeix–Raviart element discretization on the entire domain (Rui and Zhang, Comput Methods Appl Mech Eng 198:2692–2699, 2009). The a posteriori error estimate is based on a suitable evaluation on the residual of the finite element solution. It is proven that the a posteriori error estimate provided in this paper is both reliable and efficient.
We study the wave equation on a domain of $\mathbb{R}^d$, $d\geq 2$, with dynamical boundary cont... more We study the wave equation on a domain of $\mathbb{R}^d$, $d\geq 2$, with dynamical boundary control applied on a part of the boundary and a Dirichlet boundary condition on the remaining part. We prove the asymptotic stability and nonuniform stability of the associated semigroup.
The paperd#9.E with Nitsche type finite elementmethod(FEM) for treating nonmatchingmeshes at the ... more The paperd#9.E with Nitsche type finite elementmethod(FEM) for treating nonmatchingmeshes at the interface of some d# maind#9w mposition. Thismethodisappliedto some transmission (or interface) problems of the plane with Dirichlet bound# ry cond#9fiP ns presenting some corner singularities. In a natural way, the interface of the nonmatchinggrid# is taken as the interface of the problem. Properties of the finite elementschemeanderror estimates
In this Note, we study the indirect boundary stabilization of the Timoshenko system with only one... more In this Note, we study the indirect boundary stabilization of the Timoshenko system with only one dissipation law. Under the equal speed wave propagation condition, we establish the exponential stability of the system. On the contrary, we show that the decay rate is polynomial.
In this paper we develop an a posteriori error analysis of a nonconforming mixed finite element m... more In this paper we develop an a posteriori error analysis of a nonconforming mixed finite element method for the coupling of fluid flow with porous media flow. The approach utilizes the same nonconforming Crouzeix–Raviart element discretization on the entire domain (Rui and Zhang, Comput Methods Appl Mech Eng 198:2692–2699, 2009). The a posteriori error estimate is based on a suitable evaluation on the residual of the finite element solution. It is proven that the a posteriori error estimate provided in this paper is both reliable and efficient.
We study the wave equation on a domain of $\mathbb{R}^d$, $d\geq 2$, with dynamical boundary cont... more We study the wave equation on a domain of $\mathbb{R}^d$, $d\geq 2$, with dynamical boundary control applied on a part of the boundary and a Dirichlet boundary condition on the remaining part. We prove the asymptotic stability and nonuniform stability of the associated semigroup.
The paperd#9.E with Nitsche type finite elementmethod(FEM) for treating nonmatchingmeshes at the ... more The paperd#9.E with Nitsche type finite elementmethod(FEM) for treating nonmatchingmeshes at the interface of some d# maind#9w mposition. Thismethodisappliedto some transmission (or interface) problems of the plane with Dirichlet bound# ry cond#9fiP ns presenting some corner singularities. In a natural way, the interface of the nonmatchinggrid# is taken as the interface of the problem. Properties of the finite elementschemeanderror estimates
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