## Why aren't the essential boundary conditions fulfilled?

### Zoltán Csáti (view profile)

on 6 Jun 2014
Latest activity Commented on by Zoltán Csáti

on 8 Jun 2014

### Bill Greene (view profile)

I made a Poisson-solver based on Legendre-spectral method and I would like to test it. I used the pdetool, created the square region [-1,1]x[-1,1] and specified the PDE to be an elliptic one with parameters c=-1, a=0, f=x.*y. The boundary conditions: left:y, right: -y, top:-x, bottom:x. I run the task with different mesh density and obtained the interesting result that at (-1,-1) the obtained value is not -1 as it should be in my opinion. For an elliptic PDE, these Dirichlet boundary conditions are essential boundary conditions therefore they are taken into account when applying the weak form. Why aren't these boundary condition satisfied?
Thanks, Zoli

### Bill Greene (view profile)

on 6 Jun 2014

I ran this example in R2014a of MATLAB and I do get -1 at the lower left corner (and upper right)
I created the example in pdetool with the following steps: 1. Create the square. 2. After selecting Boundary Conditions, click on each edge and define r to be the values you list above (y,-y,-x,x). 3. Click the = icon.
What version of MATLAB are you running?
If you want to post your code, I'm happy to take a look.
Bill

Zoltán Csáti

### Zoltán Csáti (view profile)

on 8 Jun 2014
I examined the p and u matrices and u(1:4) gives the correct values. Then why isn't it so on the attached screenshot? It is a good lesson for me to take the returned numerical values into account and not the graphics. But why doesn't the figure show the correct values?
Bill Greene

### Bill Greene (view profile)

on 8 Jun 2014
This plotting problem was fixed in R2013a.
Bill
Zoltán Csáti

on 8 Jun 2014
Thank you.