Voir la notice de l'article provenant de la source Numdam
We study order-adaptive implementations of Hermite methods for hyperbolic and singularly perturbed parabolic initial value problems. Exploiting the facts that Hermite methods allow the degree of the local polynomial representation to vary arbitrarily from cell to cell and that, for hyperbolic problems, each cell can be evolved independently over a time-step determined only by the cell size, a relatively straightforward method is proposed. Its utility is demonstrated on a number of model problems posed in 1+1 and 2+1 dimensions.
@article{M2AN_2012__46_3_545_0,
author = {Chen, Ronald and Hagstrom, Thomas},
title = {$P$-adaptive {Hermite} methods for initial value problems},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {545--557},
publisher = {EDP-Sciences},
volume = {46},
number = {3},
year = {2012},
doi = {10.1051/m2an/2011050},
zbl = {1272.65077},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/m2an/2011050/}
}
TY - JOUR AU - Chen, Ronald AU - Hagstrom, Thomas TI - $P$-adaptive Hermite methods for initial value problems JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2012 SP - 545 EP - 557 VL - 46 IS - 3 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/m2an/2011050/ DO - 10.1051/m2an/2011050 LA - en ID - M2AN_2012__46_3_545_0 ER -
%0 Journal Article %A Chen, Ronald %A Hagstrom, Thomas %T $P$-adaptive Hermite methods for initial value problems %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2012 %P 545-557 %V 46 %N 3 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/m2an/2011050/ %R 10.1051/m2an/2011050 %G en %F M2AN_2012__46_3_545_0
Chen, Ronald; Hagstrom, Thomas. $P$-adaptive Hermite methods for initial value problems. ESAIM: Mathematical Modelling and Numerical Analysis , Special volume in honor of Professor David Gottlieb. Numéro spécial, Tome 46 (2012) no. 3, pp. 545-557. doi: 10.1051/m2an/2011050
Cité par Sources :