Hi all, The problem i’m trying to solve is: \nabla( \nabla u^2) = 0 u = 1 on \delta \Omega This is my implementation: from fenics import * mesh = UnitIntervalMesh(10) V = FunctionSpace(mesh, "CG", 1) u = Function(V) v = TestFunction(V) dt = Constant(0.1) theta = u**2 # scaling F = dot(gr…

I think you can think of this as \nabla u ^2 = 2 u \nabla u which leads to the nonlinear Poisson problem - \nabla \cdot \kappa(u) \nabla u = 0 where \kappa(u) = 2 u. This is only well posed when \kappa \neq 0 which means we need a nonzero initial guess accordingly. So try: ... u.interpolate(C…

Hi @nate thank you very much! It all makes perfect sense. The following transient problem works: from fenics import * num_steps = 3 mesh = UnitIntervalMesh(10) V = FunctionSpace(mesh, "CG", 1) u = Function(V) u_n = Function(V) v = TestFunction(V) dt = Constant(0.1) theta = u**2 theta_n = …

Formulation with grad of function squared

variational formulation

nate February 4, 2022, 2:56am 4

After you solve the system for the first time, you have a much better initial guess than a constant value of 1 everywhere. In essence you’re probably deeper in an attractor region. See some hints and tips here.

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Formulation with grad of function squared

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