Article contents
P-adaptive Hermite methods for initial value problems∗
Published online by Cambridge University Press: 11 January 2012
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.
Keywords
- Type
- Research Article
- Information
- ESAIM: Mathematical Modelling and Numerical Analysis , Volume 46 , Issue 3: Special volume in honor of Professor David Gottlieb , May 2012 , pp. 545 - 557
- Copyright
- © EDP Sciences, SMAI, 2012
References
- 7
- Cited by