# Homework Help: Weak formulation

1. Mar 31, 2009

### dirk_mec1

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 $$\eta$$ satisfying the boundary conditions and making use of IBP gives:

$$\int_0^1 \frac{d^4 u}{dx^4} \eta\ \mbox{d}x = \int_0^1 f \eta\ \mbox{d}x$$

$$\int_0^1 \frac{d^4 u}{dx^4} \eta\ \mbox{d}x = \frac{d^3 u}{dx^3} \eta\ |_0^1 - \int_0^1 \frac{d \eta}{dx} \frac{d^3 u}{dx^3}\ \mbox{d}x$$

$$= \eta|_1 - \frac{d \eta}{dx} \frac{d^2u}{dx^2}|_0^1 - \int \frac{d^2 \eta}{dx^2} \frac{d^2 u}{dx^2}\ \mbox{d}x$$

$$= \eta|_1 - \int \frac{d^2 \eta}{dx^2} \frac{d^2 u}{dx^2}\ \mbox{d}x$$

Is this correct?

Last edited by a moderator: May 4, 2017