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Partial differential Equations, Numerics and Control

Propagation of a highly oscillating wave packet through a semi-discrete media arising from a finite-differences

Aurora Mihaela Marica

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These movies represent the propagation of a highly oscillating wave packet through a semi-discrete media arising from a finite-differences, classical P1 finite-element method and, respectivelly, from a P1 discontinuous Galerkin method.

The solution of the discontinuous Galerkin method propagates acording to two dispersion relations: the physical and the spurious one. For certain values of the stabilization parameter (s=3, 5 and 25), the spurious wave propagates even in the wrong direction.

All these propagation properties of the solutions obtained by numerical schemes are related to the notion of group velocity. In the case of numerical schemes for the wave equation, the group velocity varies with respect to the wave number, whereas for the continuous case it is constant. This is the reason for which we see waves moving at different speeds.

The video from above corresponds to the stabilization parameter s=2 and the following ones to s=2.9, 3, 5 and 25 respectivelly.

This code allows to obtain these results:

[reintento.m.zip] (1 KB)
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Eusko Jaurlaritza - Gobierno Vasco ikerbasque - Basque Foundation for Science Bizkaia xede. Bizkaiko Foru Aldundia innobasque - Agencia vasca de la innovación Universidad del PaÌs Vasco (UPV/EHU)