NUEN-430 Lecture 4

Furthermore the basis functions always have the

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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 non-zero only over some small position of the mesh – usually consisting of a “few” cells. For instance, let us consider a simple 1-D spatial mesh. We will now define a piecewise-linear function ̃( ) in terms of five point values, ̃( )} { ̃( ) ∑ ( ⃗ ), where ( ⃗) { ( ⃗) { ( ⃗) Graphically, we see that { ( ⃗ ) looks as follows on the mesh interior: These are called the piecewise-linear hat functions for obvious reasons. They are interpolatory Basic functions, because the “expansion” coefficients take the form of point values of the function. Most finite-element basis functions can be put in this form. It is useful for comparing finite element and finite difference discretizations. To explain the nature of finite-element...
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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.

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