The Mathematics of Mechanobiology by Antonio DeSimone & Benoît Perthame & Alfio Quarteroni & Lev Truskinovsky

Author:Antonio DeSimone & Benoît Perthame & Alfio Quarteroni & Lev Truskinovsky
Language: eng
Format: epub
ISBN: 9783030451974
Publisher: Springer International Publishing

By considering now the strategy, we report in Fig. 3.10 the errors made for the potential and the displacement at times T = 24, 48, 96 ms. We observe that the error significantly increases for τ > 8 × 10−5 s, in particular for the potential . This is due to numerical instabilities occuring when using the semi-implicit case, which is “not guaranteed” to be stable for an arbitrary choice of τ. Nonetheless, these instabilities are “non-destructive” since the error on is not significantly affected by them. However, in both cases, we observe again that the errors are superconvergent for N sub = 1 and τ ≤ 8 × 10−5 s as they decrease quadratically. We conclude our error analysis by reporting in Fig. 3.11 the errors against Δt at time T = 96 ms when using , for different choices of N sub. We conclude that, similarly to the case, the errors converge at least linearly, as expected by the splitting schemes employed.

Fig. 3.10Errors in L 2( Ω0) (left) and L ∞( Ω0) (right) norms of the potentials (top) and of the displacements (bottom) obtained by solving the problem with , at times T = 24 ms (blue), T = 48 ms (red), and T = 96 ms (yellow), in logarithmic scale against τ, for N sub = 1

Download

Copyright Disclaimer:
This site does not store any files on its server. We only index and link to content provided by other sites. Please contact the content providers to delete copyright contents if any and email us, we'll remove relevant links or contents immediately.