Solution of Laplace equation for a regular hexagon

I am trying to solve Laplace equation in a regular hexagon. My equation is ∇2ϕ=0 and boundary conditions are :

ϕ=0 (at the base of hexagon)

ϕ=ϕ1;

ϕ=ϕ2;

ϕ=ϕ3;

ϕ=ϕ4;

ϕ=ϕ5 (the above five boundary conditions are for the remaining 5 sides.)

Now, I don't have any analytical solution for this problem. Is this solvable in MATLAB by any means. I am completely confused and don't know how to proceed.

Thanks

Answer 1

[Torsten]

http://de.mathworks.com/help/pde/index.html;jsessionid=2b1ea871d0971b1076b238044dac

Best wishes

Torsten.