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Making it work in one dimension

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Part of the Texts in Applied Mathematics book series (TAM,volume 54)

As simple as the formulations in the last chapter appear, there is often a leap between mathematical formulations and an actual implementation of the algorithms. This is particularly true when one considers important issues such as efficiency, flexibility, and robustness of the resulting methods.

In this chapter we address these issues by first discussing details such as the form of the local basis and, subsequently, how one implements the nodal DG-FEMs in a flexible way. To keep things simple, we continue the emphasis on one-dimensional linear problems, although this results in a few apparently unnecessarily complex constructions. We ask the reader to bear with us, as this slightly more general approach will pay off when we begin to consider more complex nonlinear and/or higher-dimensional problems.

Keywords

  • Legendre Polynomial
  • Jacobi Polynomial
  • Quadrature Point
  • Monomial Basis
  • Vandermonde Matrix

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© 2008 Springer Science+Business Media, LLC

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(2008). Making it work in one dimension. In: Nodal Discontinuous Galerkin Methods. Texts in Applied Mathematics, vol 54. Springer, New York, NY. https://doi.org/10.1007/978-0-387-72067-8_3

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