an:06973167
Zbl 1415.35175
Alc??ntara, Adriano A.; Clark, Haroldo R.; Rincon, Mauro A.
Theoretical analysis and numerical simulation for a hyperbolic equation with Dirichlet and acoustic boundary conditions
EN
Comput. Appl. Math. 37, No. 4, 4772-4792 (2018).
00414154
2018
j
35L20 65M60 65M06 35A01 35A02
energy decay; order of convergence of the approximate solution
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.