Abstract

We develop dissipative, energy-stable difference methods for linear first-order hyperbolic systems by applying an upwind, discontinuous Galerkin construction of derivative matrices to a space of discontinuous piecewise polynomials on a structured mesh. The space is spanned by translates of a function spanning multiple cells, yielding a class of implicit difference formulas of arbitrary order. We examine the properties of the method, including the scaling of the derivative operator with method order, and demonstrate its accuracy for problems in one and two space dimensions.

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call

Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.