Numerical solution of the Laplace equation on circular domain I was solving Laplace equation in MATLAB numerically. However I have problems when the domain is not rectangular.  
The equation is as follows:
$$
\frac{\partial^2 u}{\partial x^2}+\frac{\partial^2 u}{\partial y^2}=0
$$
domain is circular
$$
x^2 + y^2 < 16
$$
and boundary condition 
$$
u(x,y)= x^2y^2
$$
How should I start with solving this equation numerically ?

Perhaps begin by rewriting the problem in polar coordintates:
$$\frac{\partial^{2}u}{\partial r^{2}}+\frac{1}{r}\frac{\partial u}{\partial r}+\frac{1}{r^{2}}\frac{\partial^{2}u}{\partial\theta^{2}}=0$$
$$r^2<16$$
$$\left. u(r,\theta)\right|_D=r^4\cos^2\theta\sin^2\theta$$
