I am very new to fenics and I want to solve for Oseen-Frank’s well known equation for director distribution at static equilibrium using fenics.
What would be the weak form of the following nonlinear differential equation?:
(\epsilon_{\parallel} - \epsilon_{\perp}) E^2 sin(u) cos(u) + (k_{3} - k_{1})sin(u)cos(u) (\frac{d u}{d z})^2 + ( k_{1} cos^2(u) + k_{3} sin^2(u) ) \frac{d^2 u}{dz^2} = 0
Where \epsilon_{\parallel} and \epsilon_{\perp}, and k_{1} and k_{2} are constants.