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Variations on Hermite Methods for Wave Propagation

Part of: Partial differential equations, initial value and time-dependent initial-boundary value problems

Published online by Cambridge University Press:  21 June 2017

Arturo Vargas ,
Jesse Chan ,
Thomas Hagstrom  and
Timothy Warburton
Arturo Vargas*
Affiliation:
Department of Computational and Applied Mathematics, Rice University, Houston, TX 77005, USA
Jesse Chan*
Affiliation:
Department of Mathematics, Virginia Tech, Blacksburg, VA 24061, USA
Thomas Hagstrom*
Affiliation:
Department of Mathematics, Southern Methodist University, Dallas, TX 75275, USA
Timothy Warburton*
Affiliation:
Department of Mathematics, Virginia Tech, Blacksburg, VA 24061, USA
*
*Corresponding author. Email addresses:Arturo.Vargas@rice.edu (A. Vargas), jesse.chan@caam.rice.edu (J. Chan), thagstrom@mail.smu.edu (T. Hagstrom), tcew@vt.edu (T. Warburton)
*Corresponding author. Email addresses:Arturo.Vargas@rice.edu (A. Vargas), jesse.chan@caam.rice.edu (J. Chan), thagstrom@mail.smu.edu (T. Hagstrom), tcew@vt.edu (T. Warburton)
*Corresponding author. Email addresses:Arturo.Vargas@rice.edu (A. Vargas), jesse.chan@caam.rice.edu (J. Chan), thagstrom@mail.smu.edu (T. Hagstrom), tcew@vt.edu (T. Warburton)
*Corresponding author. Email addresses:Arturo.Vargas@rice.edu (A. Vargas), jesse.chan@caam.rice.edu (J. Chan), thagstrom@mail.smu.edu (T. Hagstrom), tcew@vt.edu (T. Warburton)

Abstract

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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.

Keywords

High-order methodshyperbolic problemsnumerical analysis

MSC classification

Secondary: 65M70: Spectral, collocation and related methods

Information

Type
Research Article
Information
Communications in Computational Physics , Volume 22 , Issue 2 , August 2017 , pp. 303 - 337
Copyright
Copyright © Global-Science Press 2017 

Footnotes

Communicated by Chi-Wang Shu

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