Re: [Geopdes-users] k-refinement oscilations in convergence rate

[Rafael V. <va...@im...>]

Hi Alexis,
I've tried to do the same modifying the file ex_laplace_iso_ring (see 
below). The oscillations appear around degree 17, that is much higher 
than what you usually do in IGA.

The first thing I must say is that this shouldn't be considered 
k-refinement: you have only one element, and the continuity is not 
playing any role. What you are doing is some kind of spectral method 
with NURBS. You can try to read some works on spectral methods (I'm not 
an expert) and check if they need some special technique to obtain the 
right convergence, maybe a particular quadrature rule.

But I'm also thinking that the error may come from the NURBS toolbox. I 
know that some functions in the toolbox will add rounding errors to the 
computation of the shape functions, and I guess that these errors become 
much higher for high degrees. Since I've always worked with degree lower 
than 8, I never had any problem with this. You can check if the problem 
is coming from there.

Regards,
Rafa

The problem_data is taken from ex_laplace_iso_ring. The postprocessing 
part is removed. The method data and the call to the solver are like this

method_data.nsub = [1 1];       % In this example, this is only one element!
for ii = 2:20
  method_data.degree = [ii ii];
  method_data.regularity = [ii-1 ii-1];
  method_data.nquad = [ii+1 ii+1];
  [geometry, msh, space, u] = solve_laplace_2d_iso (problem_data, 
method_data);
  [error_h1(ii), error_l2(ii)] = ...
            sp_h1_error (space, msh, u, problem_data.uex, 
problem_data.graduex);
  ndofs(ii) = space.ndof;
end
loglog(ndofs, error_l2);