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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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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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description	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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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
title	Discontinuous Galerkin Difference Methods for Symmetric Hyperbolic Systems
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