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Numerical resolution of discontinuous Galerkin methods for time dependent wave equations

✍ Scribed by Xinghui Zhong; Chi-Wang Shu

Publisher
Elsevier Science
Year
2011
Tongue
English
Weight
409 KB
Volume
200
Category
Article
ISSN
0045-7825

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✦ Synopsis

Fully discretized

Points per wavelength a b s t r a c t

The discontinuous Galerkin (DG) method is known to provide good wave resolution properties, especially for long time simulation. In this paper, using Fourier analysis, we provide a quantitative error analysis for the semi-discrete DG method applied to time dependent linear convection equations with periodic boundary conditions. We apply the same technique to show that the error is of order k + 2 superconvergent at Radau points on each element and of order 2k + 1 superconvergent at the downwind point of each element, when using piecewise polynomials of degree k. An analysis of the fully discretized approximation is also provided. We compute the number of points per wavelength required to obtain a fixed error for several fully discrete schemes. Numerical results are provided to verify our error analysis.

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