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.
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This work was supported by contracts from the U.S. Department of Energy ASCR Applied Math Program and by a U.S. Presidential Early Career Award for Scientists and Engineers. Any opinions, findings, or recommendations expressed here are those of the authors and do not necessarily reflect the views of the Department of Energy.
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Hagstrom, T., Banks, J.W., Buckner, B.B. et al. Discontinuous Galerkin Difference Methods for Symmetric Hyperbolic Systems. J Sci Comput 81, 1509–1526 (2019). https://doi.org/10.1007/s10915-019-01070-6
- Difference methods
- Galerkin methods
- Hyperbolic systems
Mathematics Subject Classification