A finite element scheme for a 2D-wave equation with dynamical boundary control

被引：2

作者：

Bzeih, Moussa ^{[1
]}

El Arwadi, Toufic ^{[1
]}

Wehbe, Ali ^{[2
]}

Madureira, Rodrigo L. R. ^{[3
]}

Rincon, Mauro A. ^{[4
]}

机构：

[1] Beirut Arab Univ, Fac Sci, Beirut, Lebanon

[2] Lebanese Univ, Fac Sci 1, Khawarizmi Lab Math & Applicat KAlMA, Beirut, Lebanon

[3] Univ Fed Rio de Janeiro, NCE, PPGI, Rio de Janeiro, Brazil

[4] Univ Fed Rio de Janeiro, Inst Computacao, Rio de Janeiro, Brazil

来源：

MATHEMATICS AND COMPUTERS IN SIMULATION | 2023年 / 205卷

关键词：

2D Wave equation; Finite element; Dynamical boundary control; ENERGY DECAY-RATE; NUMERICAL-ANALYSIS; WAVE-EQUATION; STABILIZATION; SIMULATION; PLATES;

D O I：

10.1016/j.matcom.2022.09.024

中图分类号：

TP39 [计算机的应用];

学科分类号：

081203 ; 0835 ;

摘要：

We study the 2D linear wave equation with dynamical control on the boundary. New mathematical difficulties appear due to the boundary conditions. By adding some artificial viscosity term, we introduce a penalized problem, and the well posedness is done by using the Faedo-Galerkin method. A numerical scheme is proposed and the decay of the associated discrete energy is obtained. At the end, an a priori error estimate is obtained and some numerical results are presented. (C) 2022 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.

引用

页码：315 / 339

页数：25