# Integrating until symmetric bilinear form

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1. Nov 25, 2014

### TheFerruccio

1. The problem statement, all variables and given/known data
I am looking for some quick methods to integrate while leaving each step in its vector form without drilling down into component-wise integration, and I am wondering whether it is possible here.

Suppose I have a square domain over which I am integrating two functions w and v. Using integration by parts, what steps can I use to ensure that I end up with a symmetric blinear form + boundary terms?

2. Relevant equations

$\exists$ a region $\Omega$ enclosed by $\Gamma$ and on $\Omega$ $$\int_\Omega{Tv\nabla^2 w d\Omega}=\int_\Omega{v p(x,y) d\Omega}$$

3. The attempt at a solution
Using integration by parts, whereby I feel as if I am completely guessing here:
$$T\left[v\nabla w\right]_\Gamma-T\int_\Omega{\nabla v \cdot \nabla w dV} = \int_\Omega{v p(x,y) d\Omega}$$

Is this the correct symmetric bilinear form that I am looking for? How would that simplified boundary term expression be evaluated explicitly?

2. Nov 30, 2014

### Staff: Admin

Thanks for the post! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?

3. Dec 5, 2014

### TheFerruccio

Unfortunately not. I have come to the conclusion that there is no one here who knows this particular material. It is a blend of math and engineering and computation. I will update the threads with solutions once I find them. I eventually do, but I have never gotten a single question of this area of material answered on these forums, which is a first.

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