Discontinuous Galerkin Difference Methods for Symmetric Hyperbolic Systems

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 functio...

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Bibliographic Details
Published in:Journal of scientific computing 2019-12, Vol.81 (3), p.1509-1526
Main Authors: Hagstrom, T., Banks, J. W., Buckner, B. B., Juhnke, K.
Format: Article
Language:English
Subjects:
Algorithms
Approximation
Boundary conditions
Computational Mathematics and Numerical Analysis
Galerkin method
Hyperbolic systems
Mathematical and Computational Engineering
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Methods
Operators (mathematics)
Polynomials
Theoretical
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Summary: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.
ISSN:0885-7474
1573-7691
DOI:10.1007/s10915-019-01070-6