The controllability for the semi-discrete wave equation with a finite element method
نویسندگان
چکیده
منابع مشابه
The controllability for the semi-discrete wave equation with a finite element method
*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 pr...
متن کاملA space-time finite element method for the wave equation*
where n is a bounded open domain in R d with d ffi 1, 2 and T > 0. We have restricted our attention to a specific problem entirely to keep the presentation simple. Our results apply to considerably more general second-order hyperbolic problems. Typically an approximation to (1) is found by first discretizing in space to obtain the semidiscrete problem that consists of ordinary differential equa...
متن کاملFinite Element Heterogeneous Multiscale Method for the Wave Equation
A new finite element heterogeneous multiscale method (FE-HMM) is proposed for the numerical solution of the wave equation over long times in a rapidly varying medium. Our new FE-HMM-L method not only captures the short-time behavior of the wave field, well described by classical homogenization theory, but also more subtle long-time dispersive effects, both at a computational cost independent of...
متن کاملDiscontinuous Galerkin Finite Element Method for the Wave Equation
The symmetric interior penalty discontinuous Galerkin finite element method is presented for the numerical discretization of the second-order wave equation. The resulting stiffness matrix is symmetric positive definite and the mass matrix is essentially diagonal; hence, the method is inherently parallel and leads to fully explicit time integration when coupled with an explicit timestepping sche...
متن کاملObservability 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 کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Advances in Difference Equations
سال: 2013
ISSN: 1687-1847
DOI: 10.1186/1687-1847-2013-160