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Weak formulation

  1. Mar 31, 2009 #1
    1. The problem statement, all variables and given/known data

    http://img525.imageshack.us/img525/9103/95183092.png [Broken]

    3. The attempt at a solution
    Multiplying with a testfunction [tex] \eta [/tex] satisfying the boundary conditions and making use of IBP gives:


    [tex]
    \int_0^1 \frac{d^4 u}{dx^4} \eta\ \mbox{d}x = \int_0^1 f \eta\ \mbox{d}x
    [/tex]


    [tex]
    \int_0^1 \frac{d^4 u}{dx^4} \eta\ \mbox{d}x = \frac{d^3 u}{dx^3} \eta\ |_0^1 - \int_0^1 \frac{d \eta}{dx} \frac{d^3 u}{dx^3}\ \mbox{d}x
    [/tex]


    [tex]
    = \eta|_1 - \frac{d \eta}{dx} \frac{d^2u}{dx^2}|_0^1 - \int \frac{d^2 \eta}{dx^2} \frac{d^2 u}{dx^2}\ \mbox{d}x
    [/tex]


    [tex]
    = \eta|_1 - \int \frac{d^2 \eta}{dx^2} \frac{d^2 u}{dx^2}\ \mbox{d}x
    [/tex]


    Is this correct?
     
    Last edited by a moderator: May 4, 2017
  2. jcsd
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