Abstract
We consider a system of acoustic wave equation possessing lower-order perturbation terms in a bounded domain in mathbb{R}^{2}. In this paper, we show the system is well-posed and stable with energy decays introducing a local discontinuous Galerkin (LDG) method. Also, we study an a priori L^{2}-norm error estimate for the semi-discretized LDG method for the system under additional regularity assumptions. Further, numerical tests are presented to support the theoretical analysis.
Highlights
Many phenomena of wave-type propagation with exponential decay of its amplitude can be modeled by a hyperbolic system of damped wave equations
In this paper, introducing a general formula of damped linear hyperbolic systems, we show the well-posedness of the system and present a local discontinuous Galerkin (LDG) method with its stability and a priori error estimates
The paper is organized as follows: In Sect. 2.1, we introduce a general formula for damped hyperbolic systems of the wave equation and recall couple existence theorems to show the well-posedness
Summary
Many phenomena of wave-type propagation with exponential decay of its amplitude can be modeled by a hyperbolic system of damped wave equations. Following [8], we define LDG methods for the system (2.1) considering only the spatial discretization of this equation as above. A LDG numerical method is obtained as follows.
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