Year: 2017
Communications in Computational Physics, Vol. 22 (2017), Iss. 2 : pp. 303–337
Abstract
Hermite methods, as introduced by Goodrich et al. in [15], combine Hermite interpolation and staggered (dual) grids to produce stable high order accurate schemes for the solution of hyperbolic PDEs. We introduce three variations of this Hermite method which do not involve time evolution on dual grids. Computational evidence is presented regarding stability, high order convergence, and dispersion/dissipation properties for each new method. Hermite methods may also be coupled to discontinuous Galerkin (DG) methods for additional geometric flexibility [4]. An example illustrates the simplification of this coupling for Hermite methods.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.260915.281116a
Communications in Computational Physics, Vol. 22 (2017), Iss. 2 : pp. 303–337
Published online: 2017-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 35
-
Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2018
Hermite Methods in Time
Gu, Rujie | Hagstrom, Thomas2020
https://doi.org/10.1007/978-3-030-39647-3_8 [Citations: 0] -
Leapfrog Time-Stepping for Hermite Methods
Vargas, Arturo | Hagstrom, Thomas | Chan, Jesse | Warburton, TimJournal of Scientific Computing, Vol. 80 (2019), Iss. 1 P.289
https://doi.org/10.1007/s10915-019-00938-x [Citations: 3]