Journal
JOURNAL OF COMPUTATIONAL PHYSICS
Volume 259, Issue -, Pages 1-10Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jcp.2013.11.003
Keywords
Spectral element method; Finite element method; Centred discontinuous Galerkin method; Numerical dispersion; Spurious numerical modes; Computational modes
Funding
- Isaac Newton Institute for Mathematics
Ask authors/readers for more resources
We study the ability of high order numerical methods to propagate discrete waves at the same speed as the physical waves in the case of the one-way wave equation. A detailed analysis of the finite element method is presented including an explicit form for the discrete dispersion relation and a complete characterisation of the numerical Bloch waves admitted by the scheme. A comparison is made with the spectral element method and the discontinuous Galerkin method with centred fluxes. It is shown that all schemes admit a spurious mode. The spectral element method is always inferior to the finite element and discontinuous Galerkin schemes; a somewhat surprising result in view of the fact that, in the case of the second order wave equation, the spectral element method propagates waves with an accuracy superior to that of the finite element scheme. The comparative behaviour of the finite element and discontinuous Galerkin scheme is also somewhat surprising: the accuracy of the finite element method is superior to that of the discontinuous Galerkin method in the case of elements of odd order by two orders of accuracy, but worse, again by two orders of accuracy, in the case of elements of even order. (C) 2013 Elsevier Inc. All rights reserved.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available