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P-adaptive Hermite methods for initial value problems∗

Published online by Cambridge University Press:  11 January 2012

Ronald Chen  and
Thomas Hagstrom
Ronald Chen
Affiliation:
Department of Mathematics and Statistics, The University of New Mexico, MSC03 2150, Albuquerque, 87131-0001 NM, USA. xqroy@math.unm.edu
Thomas Hagstrom
Affiliation:
Department of Mathematics, Southern Methodist University, PO Box 750156, Dallas, 75275-0156 TX, USA; thagstrom@smu.edu

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.

Keywords

Adaptivityhigh-order methods

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