Variations on Hermite Methods for Wave Propagation. (21st June 2017)

• Record Type: Journal Article
• Authors: Vargas, Arturo; Chan, Jesse; Hagstrom, Thomas; Warburton, Timothy
• Is Part Of: Communications in computational physics. Volume 22:Number 2(2017:Aug.)
• Page Start: 303
• Page End: 337
• Publication Date: 2017-06-21
• Subjects: 65M70; High-order methods, -- hyperbolic problems, -- numerical analysis; Mathematical physics -- Data processing -- Periodicals; Physics -- Data processing -- Periodicals; 530.150285
• DOI: 10.4208/cicp.260915.281116a
• Languages: English
• ISSNs: 1815-2406

Abstract

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.