I ran into a small curiosity today while attempting a simple grid refinement study. For the problem at hand, I do not have access to an analytic solution, so I am comparing solutions at gradually finer meshes to establish convergence.
I have noticed that if I create a new mesh at every refinement level, NGSolve is able to automatically interpolate the GridFunction containing the numerical solution on the old mesh onto the new mesh. However, if I use mesh.Refine(), this automatic interpolation no longer works (cf. the MWE below, where, when using mesh.Refine(), the second call to Draw simply results in a drawing of the zero function). This behavior struck me as somewhat peculiar, so I wanted to bring it to your attention in case it should be addressed somehow.
Also, if there are better ways to perform grid refinement studies in NGSolve for problems without a known analytic solution, I would be grateful for any suggestions.
from netgen.geom2d import unit_square from ngsolve.webgui import Draw import ngsolve as ng
mesh = ng.Mesh(unit_square.GenerateMesh(maxh=0.1))
V = ng.H1(mesh, order=3, dirichlet=“left|right|top”)
u,v = V.TnT()
T = ng.GridFunction(V)
a = ng.BilinearForm(V, symmetric=True)
a += ng.grad(u) * ng.grad(v) * ng.dx
f = ng.LinearForm(V)
f += 32 * (ng.y*(1-ng.y)+ng.x*(1-ng.x)) * v * ng.dx
T.vec.data = a.mat.Inverse(V.FreeDofs(), inverse=“sparsecholesky”) * f.vec
mesh.Refine() # This does NOT work
#mesh = ng.Mesh(unit_square.GenerateMesh(maxh=0.05)) # This works