A Polynomial Spectral Calculus for Analysis of DG Spectral Element Methods
arXiv:1704.0070917 citationsh-index: 33
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This work provides a new analytical tool for researchers analyzing discontinuous Galerkin spectral element methods, but the contribution is incremental as it simplifies existing analysis rather than introducing a new method or achieving new results.
The paper develops a polynomial spectral calculus based on the summation by parts property of Legendre-Gauss-Lobatto quadrature, and uses it to simplify the analysis of two multidimensional discontinuous Galerkin spectral element methods.
We introduce a polynomial spectral calculus that follows from the summation by parts property of the Legendre-Gauss-Lobatto quadrature. We use the calculus to simplify the analysis of two multidimensional discontinuous Galerkin spectral element approximations.