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

共 50 条

[21] On the coupling of finite and boundary element methods for the Helmholtz equation
Boutefnouchet, M.
Djebabla, A.
IRANIAN JOURNAL OF SCIENCE AND TECHNOLOGY TRANSACTION A-SCIENCE, 2006, 30 (A2): : 191 - 200
[22] On the Wave Equation with Hyperbolic Dynamical Boundary Conditions, Interior and Boundary Damping and Source
Vitillaro, Enzo
ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2017, 223 (03) : 1183 - 1237
[23] Uniform boundary stabilization of the finite difference space discretization of the 1−d wave equation
Louis T. Tebou
Enrique Zuazua
Advances in Computational Mathematics, 2007, 26 : 337 - 365
[24] A spectral study of the boundary controllability of the linear 2-D wave equation in a rectangle
Micu, Sorin
de Teresa, Luz
ASYMPTOTIC ANALYSIS, 2010, 66 (3-4) : 139 - 160
[25] SPACE-TIME FINITE ELEMENT METHODS FOR DISTRIBUTED OPTIMAL CONTROL OF THE WAVE EQUATION
Loscher, Richard
Steinbach, Olaf
SIAM JOURNAL ON NUMERICAL ANALYSIS, 2024, 62 (01) : 452 - 475
[26] On an optimal boundary control problem for 1-D wave equation with a damping boundary condition
Kholomeeva, A. A.
Moiseev, E., I
39TH INTERNATIONAL CONFERENCE APPLICATIONS OF MATHEMATICS IN ENGINEERING AND ECONOMICS (AMEE13), 2013, 1570 : 241 - 248
[27] Exact controllability of the interconnected Schrodinger and wave equations with a boundary control at the wave equation
Wang, Fei
Wang, Jun-Min
Wu, Xiao-Hui
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2023, 519 (02)
[28] Numerical wave tanks based on finite element and boundary element modeling
Taylor, R. Eatock
Wu, G. X.
Bai, W.
Hu, Z. Z.
JOURNAL OF OFFSHORE MECHANICS AND ARCTIC ENGINEERING-TRANSACTIONS OF THE ASME, 2008, 130 (03):
[29] FINITE ELEMENT HETEROGENEOUS MULTISCALE METHOD FOR THE WAVE EQUATION
Abdulle, Assyr
Grote, Marcus J.
MULTISCALE MODELING & SIMULATION, 2011, 9 (02) : 766 - 792
[30] Numerical wave tanks based on finite element and boundary element modelling
Taylor, R. Eatock
Wu, G. X.
Bai, W.
Hu, Z. Z.
PROCEEDINGS OF THE 24TH INTERNATIONAL CONFERENCE ON OFFSHORE MECHANICS AND ARCTIC ENGINEERING, VOL 3, 2005, : 1003 - 1010

← 1 2 3 4 5 →