A Finite Element Method for a Non-linear Initial Value Problem

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Abstract
A linear finite element method is applied to the shallow water equations using a grid of equilateral triangles. The method is found to give a very accurate description of the flow while most of the energy is contained in disturbances extending over at least four elements and is competitive in time with finite difference schemes provided that the resolution is sufficient for the energy spectrum of the problem. While in some cases finite element methods lead to well-known finite difference approximations, it is shown that they lead to more advantageous schemes for non-linear terms, and make the best use of the available data.

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