How to solve a problem based on 2D polar coordinate

General Discussion
1

Hello, everyone. I’m solving a problem in a domain which is reprensted with polar coordinate. The equation is given in rectangular coordinate system. But the Dirichlet boundary condition is polar coordinate. So I think I should solve this equation in polar coordinate. But I don’t know if freefem can solve 2D coordinate equations. If the answer is yes, how should the two polar variables be represented in freefem. I’m looking forward to receiving your reply. Thank you very much!

2

Page 52 of the FreeFem++ Documentation talks about the polar coordinate system. Here is an exaple of how the Laplace operator is defined:

problem thermaxi(u, v)
 = int2d(Th)(
 (u*v/dt + dx(u)*dx(v) + dy(u)*dy(v))*x
 )
 + int1d(Th, 3)(
 alpha*x*u*v
 )
 - int1d(Th, 3)(
 alpha*x*ue*v
 )
 - int2d(Th)(
 uold*v*x/dt
 )
 + on(2, 4, u=u0);