Why aren't the essential boundary conditions fulfilled?

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Zoltán Csáti 2014-6-6

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评论： Zoltán Csáti 2014-6-8

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

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Bill Greene 2014-6-6

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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