The controllability for the semi-discrete wave equation with a finite element method

نویسندگان

  • Guojie Zheng
  • Xin Yu
چکیده

*Correspondence: [email protected] 3Ningbo Institute of Technology, Zhejiang University, Ningbo, 315100, P.R. China Full list of author information is available at the end of the article Abstract In this paper, we study the controllability problem of the semi-discrete internally controlled one-dimensional wave equation with the finite element method. We derive the observability inequality and prove the exact controllability for the semi-discrete internally controlled wave equation, with the controls taken from a finite dimensional space. MSC: 49K20; 35J65

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

A new positive definite semi-discrete mixed finite element solution for parabolic equations

In this paper, a positive definite semi-discrete mixed finite element method was presented for two-dimensional parabolic equations. In the new positive definite systems, the gradient equation and flux equations were separated from their scalar unknown equations.  Also, the existence and uniqueness of the semi-discrete mixed finite element solutions were proven. Error estimates were also obtaine...

متن کامل

Observability Properties of a Semi-discrete 1d Wave Equation Derived from a Mixed Finite Element Method on Nonuniform Meshes

The goal of this article is to analyze the observability properties for a space semi-discrete approximation scheme derived from a mixed finite element method of the 1d wave equation on nonuniform meshes. More precisely, we prove that observability properties hold uniformly with respect to the mesh-size under some assumptions, which, roughly, measures the lack of uniformity of the meshes, thus e...

متن کامل

Solution of Wave Equations Near Seawalls by Finite Element Method

A 2D finite element model for the solution of wave equations is developed. The fluid is considered as incompressible and irrotational. This is a difficult mathematical problem to solve numerically as well as analytically because the condition of the dynamic boundary (Bernoulli’s equation) on the free surface is not fixed and varies with time. The finite element technique is applied to solve non...

متن کامل

Optimal order finite element approximation for a hyperbolic‎ ‎integro-differential equation

‎Semidiscrete finite element approximation of a hyperbolic type‎ ‎integro-differential equation is studied. The model problem is‎ ‎treated as the wave equation which is perturbed with a memory term.‎ ‎Stability estimates are obtained for a slightly more general problem.‎ ‎These, based on energy method, are used to prove optimal order‎ ‎a priori error estimates.‎

متن کامل

Uniform Boundary Controllability of a Semidiscrete 1-D Wave Equation with Vanishing Viscosity

This article deals with the approximation of the boundary control of the linear onedimensional wave equation. It is known that the high frequency spurious oscillations that the classical methods of finite difference and finite element introduce lead to nonuniform controllability properties (see [J. A. Infante and E. Zuazua, M2AN Math. Model. Numer. Anal., 33 (1999), pp. 407–438]. A space-discre...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2013