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Unformatted text preview: e original equation with the residual as the source
term. Thus, the error is indeed proportional to the residual.
There are three primary finite element techniques for making the residual small.
Choose the expansion coefficients so that:
()
a.
b. ∫ ( )
{}
c. ∫ ( ( ) , for some set of distinct points { ̃ }
. This is called collocation.
()
for some set of N linearlyindependent weighting functions,
. This is called the weighted residual method.
∑ ( ⃗ )) is minimized. This is called the leastsquares method. It is not obvious as to how the weighted residual method makes the residual “small”. It can be shown
that if one does a leastsquares fit to the residual using the weight functions, the fit will be equal to the
zero function. This is not to be confused with the leastsquares method.
For instance, suppose I want to do a leastsquares fit to an arbi...
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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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