NUEN-430 Lecture 4

Thus the error is indeed proportional to the residual

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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 linearly-independent weighting functions, . This is called the weighted residual method. ∑ ( ⃗ )) is minimized. This is called the least-squares 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 least-squares 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 least-squares method. For instance, suppose I want to do a least-squares 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.

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