Approximation of acoustic waves by explicit Newmark’s schemes and spectral element methods. (English) Zbl 1079.65093

Zampieri, Elena; Pavarino, Luca F.

J. Comput. Appl. Math. 185, No. 2, 308-325 (2006).

The acoustic wave equation is numerically approximated by conforming spectral elements in space and a finite difference Newmark‘s explicit integration scheme in time. A rigorous stability analysis is developed providing an upper bound for the time step. Several numerical results concerning stability and convergence of the proposed method are presented.

Reviewer: Wilhelm Heinrichs (Essen)

MSC:

65M06	Finite difference methods for initial value and initial-boundary value problems involving PDEs
65M70	Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
65M12	Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
35L05	Wave equation
76Q05	Hydro- and aero-acoustics
76M20	Finite difference methods applied to problems in fluid mechanics
76M22	Spectral methods applied to problems in fluid mechanics

Keywords:

spectral elements; Newmark’s explicit schemes; acoustic wave equation; finite difference; stability; numerical results; convergence

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