Volume 22, Issue 2
Variations on Hermite Methods for Wave Propagation

Arturo Vargas, Jesse Chan, Thomas Hagstrom & Timothy Warburton

Commun. Comput. Phys., 22 (2017), pp. 303-337.

Published online: 2018-04

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  • 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.

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@Article{CiCP-22-303, author = {}, title = {Variations on Hermite Methods for Wave Propagation}, journal = {Communications in Computational Physics}, year = {2018}, volume = {22}, number = {2}, pages = {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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.260915.281116a}, url = {http://global-sci.org/intro/article_detail/cicp/11300.html} }
TY - JOUR T1 - Variations on Hermite Methods for Wave Propagation JO - Communications in Computational Physics VL - 2 SP - 303 EP - 337 PY - 2018 DA - 2018/04 SN - 22 DO - http://doi.org/10.4208/cicp.260915.281116a UR - https://global-sci.org/intro/article_detail/cicp/11300.html KW - AB -

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.

Arturo Vargas, Jesse Chan, Thomas Hagstrom & Timothy Warburton. (2020). Variations on Hermite Methods for Wave Propagation. Communications in Computational Physics. 22 (2). 303-337. doi:10.4208/cicp.260915.281116a
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