P-adaptive Hermite methods for initial value problems∗

Ronald Chen; Thomas Hagstrom

ESAIM: Mathematical Modelling and Numerical Analysis (2012)

  • Volume: 46, Issue: 3, page 545-557
  • ISSN: 0764-583X

Abstract

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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.

How to cite

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Chen, Ronald, and Hagstrom, Thomas. "P-adaptive Hermite methods for initial value problems∗." ESAIM: Mathematical Modelling and Numerical Analysis 46.3 (2012): 545-557. <http://eudml.org/doc/277844>.

@article{Chen2012,
abstract = {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.},
author = {Chen, Ronald, Hagstrom, Thomas},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Adaptivity; high-order methods; adaptivity; hyperbolic equations; parabolic equations; singular perturbation; numerical examples; Hermite methods; initial value problems},
language = {eng},
month = {1},
number = {3},
pages = {545-557},
publisher = {EDP Sciences},
title = {P-adaptive Hermite methods for initial value problems∗},
url = {http://eudml.org/doc/277844},
volume = {46},
year = {2012},
}

TY - JOUR
AU - Chen, Ronald
AU - Hagstrom, Thomas
TI - P-adaptive Hermite methods for initial value problems∗
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2012/1//
PB - EDP Sciences
VL - 46
IS - 3
SP - 545
EP - 557
AB - 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.
LA - eng
KW - Adaptivity; high-order methods; adaptivity; hyperbolic equations; parabolic equations; singular perturbation; numerical examples; Hermite methods; initial value problems
UR - http://eudml.org/doc/277844
ER -

References

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