1. Examples in dimension 1
Dimension 1 space has the advantage that some of the difficulties usually encountered when analyzing finite volume methods are absent. Nevertheless, the construction technique is clear and serves as a guide for more complex cases.
1.1 Transport
As its name suggests, the transport equation models the "transport" of a quantity noted c, as concentration, under the action of a velocity field noted ν, as velocity. We distinguish the case of a constant velocity field, in which case it's the advection equation.
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Examples in dimension 1
Dimension 2
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