How to smoothen a function on the boundary

1

Hi all,

I have a time dependent function that starts acting rather strange on the boundary after some time. Below is an image of it using Warp by Scalar feature in Paraview.

Capture
Capture207×539 7.47 KB

You can see how jagged it is at the boundary. These are things I have done and hasn’t worked:
1- I have used projections onto spaces with CR, CG and DG elements with low and high degrees. But it didn’t help.
2- I have used very fine mesh close to the boundary but it didn’t work.
3- I have used mesh and boundary smoothing at each time step and that didn’t work.
4- I have done all of the above together with no luck.
I was thinking about replacing the values of the function at the boundary with the average of the function over the boundary but I don’t know how to do so. Can you send me a mini code that does that? Or let me know if you have other easier suggestions to solve this problem.

Best,

2

It would be helpful if you could provide more context (i.e. the function you’re attempting to discretise) and a MWE.

3

Well. The function comes from a complex system of PDEs. But if you can make it work for the following It can be done for my case as well. Suppose you don’t know where the function f comes from. How can you set its value on the boundary to be the average of its current values on the boundary?

from dolfin import *
meshlevel =10
degree = 1
dim = 2
mesh = UnitDiscMesh.create(MPI.comm_world, meshlevel, degree, dim)

S = FunctionSpace(mesh,'P',1)

F = Expression('exp(cos(10*x[0])*sin(10*x[1]))',degree=0)

f = project(F,S)

File('test/test.pvd')<<f