Abstract
In this chapter we describe the implementation of the continuous Galerkin (CG) method. We show how this method can be used for the 1D wave equation which is representative of hyperbolic equations. It will be shown why we needed to spend time in Ch. 3 on interpolation and in Ch. 4 on numerical integration. Although we only focus on scalar equations in this chapter, it should be understood that the same approach can be used to discretize systems of hyperbolic equations. We tackle systems of nonlinear hyperbolic equations in Ch. 7. In particular we discuss the discretization of both the CG and DG methods for 1) the shallow water equations and 2) the Euler equations. However, in order to understand how to use the CG method for such systems we must first understand how to apply CG to a scalar equation.
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Giraldo, F.X. (2020). 1D Continuous Galerkin Method for Hyperbolic Equations. In: An Introduction to Element-Based Galerkin Methods on Tensor-Product Bases. Texts in Computational Science and Engineering, vol 24. Springer, Cham. https://doi.org/10.1007/978-3-030-55069-1_5
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DOI: https://doi.org/10.1007/978-3-030-55069-1_5
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Publisher Name: Springer, Cham
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Online ISBN: 978-3-030-55069-1
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