Unformatted text preview: o derivatives. Unknowns are point values of the solution.
Finite volume schemes are a subclass of finite difference schemes that are applied to balance or
conservation equations. Most finite difference approximations used in nuclear engineering are
of this type. The basic idea behind these schemes is to ensure that the discrete approximation
makes a statement of conservation on each mesh cell in analogy with the fact that the analytic
equation makes a statement of conservation over each differential volume.
Finite element methods are based upon the use of finitedimensional function spaces to
approximate the solution to the differential equations. This sounds sophisticated, but an
element of a function space is just a function, ̃( ) , that is defined in terms of a set of Basis
functions, { ( ⃗ )}
and an associated set of coefficients, { }
. Thus, ̃( ) ∑ ( ⃗) A finiteelement basis set is always related to a mesh structure, and the expansion coefficients
often take the form of discrete val...
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 Fall '10
 Morel
 Numerical Analysis, Partial differential equation, finite difference, discretization, approximate solution

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