$P$-adaptive Hermite methods for initial value problems
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 46 (2012) no. 3, p. 545-557

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.

DOI : https://doi.org/10.1051/m2an/2011050
Classification:  65M70,  65M12
Keywords: adaptivity, high-order methods
@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 - Mod\'elisation Math\'ematique et Analyse Num\'erique},
publisher = {EDP-Sciences},
volume = {46},
number = {3},
year = {2012},
pages = {545-557},
doi = {10.1051/m2an/2011050},
zbl = {1272.65077},
language = {en},
url = {http://www.numdam.org/item/M2AN_2012__46_3_545_0}
}

Chen, Ronald; Hagstrom, Thomas. $P$-adaptive Hermite methods for initial value problems. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 46 (2012) no. 3, pp. 545-557. doi : 10.1051/m2an/2011050. http://www.numdam.org/item/M2AN_2012__46_3_545_0/

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