6a-Galerkin Method-2010s

6a-Galerkin Method-2010s - William Klug MAE M168/CEE M135C...

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Unformatted text preview: William Klug MAE M168/CEE M135C Introduction to Finite Element Methods Lecture 6a Approximation Techniques: Galerkin Method William Klug Galerkin Method One member of the family of weighted residual approximation methods. Assume an approximate solution which takes the following form: u u x ( ) u = c i i x ( ) i = 1 N ( ) : chosen basis function (admissible) i x : unknown amplitude i c William Klug Residual Error Function Formed directly by replacing with in the differential equation governing the problem. Residual measures error No choice of c i make error zero. u u ( ) ( ) ( ) 0 d du R x L u q L u EA dx dx = + = William Klug Unknown Coefficients c i Try to make error zero in the average sense: weighted residual Not possible for all v ( x ) (Fund. Lemma C.V.). Instead, do it for a set of N particular weight functions....
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This note was uploaded on 08/09/2011 for the course MAE 168 taught by Professor Klug during the Spring '11 term at UCLA.

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6a-Galerkin Method-2010s - William Klug MAE M168/CEE M135C...

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