Publication

Spectral Discontinuous Galerkin Method for Hyperbolic Problems

2005
Student Projects

Abstract

In this project we address the numerical approximation of hyperbolic equations and systems using the discontinuous Galerkin (DG) method in combination with higher order polynomial degrees. In short, this is called Spectral Discontinuous Galerkin (SDG) method. Our interest is to review the theoretical properties of the SDG-method, particularly for what concerns stability, convergence, dissipation and dispersion. Special emphases will be shed on the role of the two parameters,(the grid-size) and (the local polynomial degree). In this respect, we will carefully analyse the available theoretical results from the literature, then we extend some of them and implement several test cases with the purpose of assessing quantitatively the predicted theoretical properties.

Official source

https://infoscience.epfl.ch/entities/publication/38dab289-d354-4a58-b320-4b0cbbefa88c

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2005
Student Projects

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/38dab289-d354-4a58-b320-4b0cbbefa88c

About this result

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Numerical stability

In the mathematical subfield of numerical analysis, numerical stability is a generally desirable property of numerical algorithms. The precise definition of stability depends on the context. One is numerical linear algebra and the other is algorithms for solving ordinary and partial differential equations by discrete approximation. In numerical linear algebra, the principal concern is instabilities caused by proximity to singularities of various kinds, such as very small or nearly colliding eigenvalues.

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Spectral Discontinuous Galerkin Method for Hyperbolic Problems

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