Nonlinear systems of PDE's

mathematics
4

You can deal with this by 2 approaches.

  1. Use the below piece of code to generate the mesh using mshr (not maintained any longer, therefore can use UnitSquareMesh(n, n) if mshr doesn’t work).
from dolfin import *
from mshr import *
domain=Rectangle(Point(-0.5,-0.5),Point(0.5,0.5))-Rectangle(Point(-0.5,-0.0001),Point(0,0.0001))
mesh=generate_mesh(domain,10)

and refine mesh at the crack tip using the code given here.
Reference : Phase Field Fracture

  1. You can use Gmsh and take advantage of increasing mesh field at a point. After doing meshing, you can export file in .msh format and then refer to Transitioning from mesh.xml to mesh.xdmf, from dolfin-convert to meshio on how to import this mesh.

Which version are you talking about ? If I remember the paper has only one code version that you are using.

I’ll look into it when am able to, but one thing I can tell that this form doesn’t match with what you wrote in mathematics above.

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