Abstract
Before we can understand the nuances of the various methods for discretizing nonlinear partial differential equations in space, we must first realize the choices that we have at our disposal. We can categorize the possible methods as follows:
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1.
methods that use the differential form of the equations and
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2.
methods that use the integral form of the equations.
Generally speaking, the most widely used differential form method is the finite difference method while the most widely used integral form method is the Galerkin method (e.g., finite elements).
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Giraldo, F.X. (2020). Overview of Galerkin Methods. 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_2
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DOI: https://doi.org/10.1007/978-3-030-55069-1_2
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Publisher Name: Springer, Cham
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