Numerical approximation of acoustic waves by spectral element methods

Authors:
Zhijian Rong;Chuanju Xu
Affiliations:
School of Mathematical Sciences, Xiamen University, China;School of Mathematical Sciences, Xiamen University, China
Venue:
Applied Numerical Mathematics
Year:
2008

Citing 7
Cited 0

An explicit finite element method for the wave equation

Applied Numerical Mathematics - Special issue: a festschrift to honor Professor Robert Vichnevetsky on his 65th birthday
The P and H-P versions of the finite element method, basic principles and properties

SIAM Review
A continuous space-time finite element method for the wave equation

Mathematics of Computation
A Domain Decomposition Method for the Acoustic Wave Equation with Discontinuous Coefficients and Grid Change

SIAM Journal on Numerical Analysis
A Priori Error Estimates for Mixed Finite Element Approximations of the Acoustic Wave Equation

SIAM Journal on Numerical Analysis
Investigation of a two-dimensional spectral element method for Helmholtz's equation

Journal of Computational Physics
Spectral Approximation of the Helmholtz Equation with High Wave Numbers

SIAM Journal on Numerical Analysis

Quantified Score

Hi-index	0.00

Visualization

Abstract

In this paper we consider the approximation of acoustic wave propagation problems. Precisely, we investigate the stability and convergence of the classical Newmark schema in time and spectral element discretization in space for the wave problems. A special attention is payed to the non-homogeneous boundary data. Some detailed error estimates are obtained. From these results, the spectral accuracy and influences of the non-homogeneous boundary data are made evident. Several numerical examples are provided to confirm our theoretical analysis. The advantage of the present method is demonstrated by a numerical comparison with the finite element method.