Lecture10-18-10

Lecture10-18-10 - H 1 0, ( ) Since v H 1 0, ( ) , we can...

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ECE 715: I NTRO . TO CEM – F INITE E LEMENT M ETHOD Galerkin Weak Formulation: Determine the trial function space: u H 0 1 0, π ( ) Associate with every trial function, u x ( ) H 0 1 0, ( ) , a residual: R x ( ) : = d dx p x ( ) du x ( ) dx + q x ( ) u x ( ) f x ( ) Construct the test function, being the dual to the residual space: v H 0 1 0, ( ) The weak solution is the one whose residual is orthogonal to every test function: v ( x ) R x ( ) dx = 0; v
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Unformatted text preview: H 1 0, ( ) Since v H 1 0, ( ) , we can perform the integration-by-part: dv x ( ) dx p x ( ) du x ( ) dx + v x ( ) q x ( ) u x ( ) dx = v x ( ) f x ( ) dx v H 1 0, ( ) V ARIATIONAL F ORMULATION L AX-M ILGRAM T HEOREM E RRORS IN F INITE E LEMENT M ETHODS...
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Lecture10-18-10 - H 1 0, ( ) Since v H 1 0, ( ) , we can...

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