Theoretical analysis and numerical simulation for a hyperbolic equation with Dirichlet and acoustic boundary conditions

This paper is concerned with a theoretical and numerical study for the initial-boundary value problem for a linear hyperbolic equation with variable coefficient and acoustic boundary conditions. On the theoretical results, we prove the existence and uniqueness of global solutions, and the uniform st...

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Bibliographic Details
Published in:Computational & applied mathematics 2018-09, Vol.37 (4), p.4772-4792
Main Authors: Alcântara, Adriano A., Clark, Haroldo R., Rincon, Mauro A.
Format: Article
Language:English
Subjects:
Applications of Mathematics
Applied physics
Boundary conditions
Boundary value problems
Computational mathematics
Computational Mathematics and Numerical Analysis
Computer simulation
Decay rate
Dirichlet problem
Finite difference method
Finite element method
Mathematical Applications in Computer Science
Mathematical Applications in the Physical Sciences
Mathematics
Mathematics and Statistics
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Summary:This paper is concerned with a theoretical and numerical study for the initial-boundary value problem for a linear hyperbolic equation with variable coefficient and acoustic boundary conditions. On the theoretical results, we prove the existence and uniqueness of global solutions, and the uniform stability of the total energy. Numerical simulations using the finite element method associated with the finite difference method are employed, for one-dimensional and two-dimensional cases, to validate the theoretical results. In addition, numerically the uniform decay rate for energy and the order of convergence of the approximate solution are also shown.
ISSN:0101-8205
2238-3603
1807-0302
DOI:10.1007/s40314-018-0601-y