On a nonlinear problem with Dirichlet and Acoustic boundary conditions

Adriano A. Alcântara, Bruno A. Carmo, Haroldo R. Clark, Ronald R. Guardia and Mauro A. Rincon

Applied Mathematics and Computation, 2021, vol. 411, issue C

Abstract: The aims of this paper are to establish theoretical analysis and numerical simulation for a nonlinear wave equation with mixed boundary conditions of Dirichlet and Acoustic type. The theoretical results are about: existence and uniqueness of global solutions, regularity and uniform stability of these global solutions and an exponential decay rate for energy. In the numerical context, simulations are presented using the finite element method in space (with linear and quadratic Lagrange basis), the Crank-Nicolson method in time and, for each discrete time, the Newton’s method is used to solve the nonlinear algebraic system. Furthermore, the energy exponential decay and convergence order (sub-optimal and optimal) are presented numerically.

Keywords: Existence and uniqueness of solutions; Acoustic boundary conditions; Energy exponential decay; Finite element method; Crank-Nicolson method; Newton’s method (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0096300321006032
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:411:y:2021:i:c:s0096300321006032

DOI: 10.1016/j.amc.2021.126514

Access Statistics for this article

Applied Mathematics and Computation is currently edited by Theodore Simos

More articles in Applied Mathematics and Computation from Elsevier
Bibliographic data for series maintained by Catherine Liu ().