i am trying to calculate error and convergence in terms of mesh. how do i do it, any help, how to refine the mesh is the problem in the for loop. This the mesh mesh = RectangleMesh(Point(0.0, 0.0),Point(2.0math.pi, 2.0math.pi),2**(6), 2**(6))

That is trivial: for i in range(2,8): mesh = RectangleMesh(Point(0.0, 0.0),Point(2.0math.pi, 2.0math.pi),2**(i), 2**(i)),

You can use mesh=refine(mesh) inside the loop

Does that include changing the dimension of x and y or i have to define that as well

For a convergence study, it is common to have a mesh of the same area, and increasing the number of elements describing this area. Refining the mesh will keep the same outer boundaries, But increase the «resolution» of your discretization.

ok, i do understand but it gives error and as well, with the mesh define above, i would like to know how to just change the values of the mesh without using the mesh=refine (mesh)

What do you mean by changing the values of the mesh? A mesh connsists of points, and cells (connectivity between points). You can either move the points, (without changing connectivity), add more points and change connectivity with either doing refine or remeshing

i want to know how to do mesh convergence, i am trying to write a code in spatial discretization. the mesh i used was rectangle, which is mesh = RectangleMesh(Point(0.0, 0.0),Point(2.0math.pi, 2.0math.pi),2**(6), 2**(6)), want to know how to change the point ((2**(6), 2**(6)) to say [4, 8, 16, 32…

how to i then compute the error, since the mesh are not equal. how do i interpolate the mesh to be able to compute the error and rate of convergence.

It Depends on what error you are measuring. If you are measuring against an exact solution, you can do e_i = assemble((uh-u_ex)**2*dx(domain=mesh_i)) Where the convergence rate is r=log(e_i/e_{i-1})/log(h_i/h_{i-1}) Where h_i is the largest celldiameter in mesh_i. This is the normal way of compu…

Maybe you have a function named ‘ch’ elsewhere in your code? What happens if you try different name? And for interpolating last solution obtained, try looking at the previous post on projecting data from one mesh to other. Once projected, do as you would do with exact solution.

how do you interpolate unto same space

Mesh refinement

mesh

dokken March 13, 2020, 8:52pm 15

As i said earlier, use the LagrangeInterpolator:

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Mesh refinement

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