Periodic condition in FEM space

General Discussion
1

Hi everybody,

I want to know how the function “periodic” work in FEM space.

For example, If I define fespace Vh(Th, P1, periodic = [[1, x], [3, x], [2, y], [4, y]]) with mesh Th = square(2, 2). Is it equivalent to define fespace Vh(Th, P1), and just force the degrees of freedom on 1, 3 sides to be equal (so are 2,4 sides)？

Best regards.

2

Yes, that is correct. There are multiple examples with periodic BC in the examples folder of FreeFEM if you need.

3

Thanks @prj for your reply.

I wrote two files about this，
test1.edp (505 Bytes)
test2.edp (1.3 KB)
I am confused that I get different results , could you please check it?

4

test1.edp is correct, test2.edp is wrong.

5

Is there any error in the finite element interpolation in test2.edp? I tried to achieve the same result as test1.edp without using function “periodic”, but failed.

6

I have no idea of what you are doing in test2.edp.

7

I will check it carefully. Thank you so much again @prj