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6a-Galerkin Method-2010s

# 6a-Galerkin Method-2010s - MAE M168/CEE M135C Introduction...

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© William Klug MAE M168/CEE M135C Introduction to Finite Element Methods Lecture 6a Approximation Techniques: Galerkin Method

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© 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 φ i x ( ) i = 1 N ( ) : chosen basis function (admissible) i x φ :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 = + =

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© 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. N equations in N unknown coefficients c i . 0
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6a-Galerkin Method-2010s - MAE M168/CEE M135C Introduction...

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