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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