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Unformatted text preview: ues of ̃( ) on the mesh. Furthermore, the Basis functions always have the property of local support. This means that each basis function is nonzero only
over some small position of the mesh – usually consisting of a “few” cells.
For instance, let us consider a simple 1D spatial mesh. We will now define a piecewiselinear function ̃( ) in terms of five point values,
̃( )} { ̃( ) ∑ ( ⃗ ), where ( ⃗) { ( ⃗)
{ ( ⃗) Graphically, we see that { ( ⃗ ) looks as follows on the mesh interior: These are called the piecewiselinear hat functions for obvious reasons. They are interpolatory
Basic functions, because the “expansion” coefficients take the form of point values of the
function. Most finiteelement basis functions can be put in this form. It is useful for comparing
finite element and finite difference discretizations.
To explain the nature of finiteelement...
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This note was uploaded on 10/06/2013 for the course NEUN 430 taught by Professor Morel during the Fall '10 term at Texas A&M.
 Fall '10
 Morel

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