Solve PDE - elliptic equation

2016 11 13

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Hi, I have to solve this PDE:

Uxx+Uxy+Uyy+sin(u)=12∗(x2+y2)+sin(x2+y2)Uxx+Uxy+Uyy+sin(u)=12∗(x2+y2)+sin(x2+y2)

The domain is

U(0,y)=y4;U(1,y)=1+y4;U(x,0)=x4;U(x,1)=1+x4;U(0,y)=y4;U(1,y)=1+y4;U(x,0)=x4;U(x,1)=1+x4;

First of all I think that I change the equations in canonical form, I do this with:

(eta=((3)(1/2)x/2),(ξ=y−(1/2)x):(eta=((3)(1/2)x/2),(ξ=y−(1/2)x):

This is quite easy. The problem is the domain: How can I transform in the new coordinates?

I need a domain that is rectangular: I want to solve the equation with Jacobi iterative method.

Thanks

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Torsten 2016-11-15

If the domain is rectangular for the original equation, it's better to leave everything as it is. Schemes to discretize Uxy are standard.

Best wishes

Torsten.

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